Considerations in proteomic mass spectranormalisation

Tyman StanfordProfessor Patty SolomonDr Chris Bagley

July 10, 2012

SCHOOL OF

MATHEMATICAL SCIENCES

Motivation

I Find biomarkers of disease

I In this context, using proteomicsI via mass spectrometry

I Unfortunately the data aren’t ‘good-to-go’

I Currently there are no standard methods to make it so

The technology

The data

Pre-processing

NormalisationCurrent standardsCyclic LOESS

Some results

MALDI-TOF MS

MALDI Matrix assisted laser desorption/ionisationTOF Time-of-flightMS Mass spectrometry

The data

Proteomic TOF-MS produces data:

I observed intensities/counts (y -axis)

I proteins across a mass/charge range (x-axis).

For simplicity, consider the spectrum as a profile of abundance ofproteins over a range of molecular weights (in Daltons).

Mass/charge is abbreviated as m/z.

But the raw data cannot be interpreted as such

m/z

Inte

nsity

2000 4000 6000 8000 10000 12000

01

23

45

6

Non−biological signal

Electrical noise

Matrix molecule?

Arbitrary units

Feature selection

Protein identification/classification

Analysis

�x11 x12

x21 x22

�Patient

m/z

Denoising

Baseline subtraction

Normalisation

Peak detection/alignment

Pre-processing

The data after smoothing and baseline subtraction

m/z

Inte

nsity

2000 4000 6000 8000 10000

025

025

025

Patient 12

Patient 45

Patient 76

Zooming in...

m/z

Inte

nsity

2600 2800 3000 3200 3400

05

05

05

Patient 12

Patient 45

Patient 76

And again...

m/z

Inte

nsity

3240 3250 3260 3270 3280 3290

05

05

05

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●

●

●

●

●

●

●

●●

●●

●●

●●

● ● ● ● ● ● ● ● ● ●●

●●

●●

●●

●

●

●

●

●

●●

●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

Patient 12

● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●● ● ● ● ● ● ●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

Patient 45

● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

Patient 76

Normalisation

Each spectrum from each patient will have variable received signal

I Normalisation is method to make sure realised signal isreflective of true peptide expression

I A result of difference in desorbed ions

I There will be differences across spectra

I Also remove any other systematic intensity differences (e.g..local adjustment of peak intensities)

Normalisation

Each spectrum from each patient will have variable received signal

I Normalisation is method to make sure realised signal isreflective of true peptide expression

I A result of difference in desorbed ionsI There will be differences across spectra

I Also remove any other systematic intensity differences (e.g..local adjustment of peak intensities)

Normalisation

Each spectrum from each patient will have variable received signal

I Normalisation is method to make sure realised signal isreflective of true peptide expression

I A result of difference in desorbed ionsI There will be differences across spectra

I Also remove any other systematic intensity differences (e.g..local adjustment of peak intensities)

Normalisation

In MS research there have only been simple normalisation methodssuggested to adjust spectra

I Total Ion Current (TIC)

I Mapping of percentiles within spectra to [0,1]

I Standard normal variate

Normalisation

In MS research there have only been simple normalisation methodssuggested to adjust spectra

I Total Ion Current (TIC)

I Mapping of percentiles within spectra to [0,1]

I Standard normal variate

Normalisation

In MS research there have only been simple normalisation methodssuggested to adjust spectra

I Total Ion Current (TIC)

I Mapping of percentiles within spectra to [0,1]

I Standard normal variate

TIC normalisation

Works by

I Summing the total intensities (little histograms) of a spectrum

I Do this for all spectra

I Find the mean TIC

I Multiply each spectrum by the mean TIC and divide by itsown TIC

Yi ← Yi ×1n

∑nj=1 TIC (Yj)

TIC (Yi )

TIC normalisation

TIC normalisation has theoretically good overall characteristics

I But wont adjust individual peaks or subsections along thespectra

I i.e. its global adjustment but not local adjustment forlocation-dependent signal

I That may be caused by the system or the pre-processing

Cyclic LOESS

Cyclic LOESS offers an alternative for normalisation that can alsoaccount for systematic differences in peptide expression

I Local adjustments

CLN

Cyclic LOESS Normalisation (CLN) is used in the microarrayliterature

I CLN will be a novel method for MS

I We locally adjust for peak intensities that may be artefacts ofthe system (desorption, detection)

CLN

How do we locally adjust peak intensities?

I Consider a pairwise comparison of two spectra

I Let the first spectra, i , have the intensity Yi ,t at mass t

I Similarly Yj ,t for the second spectra

Now define the values:

Mt = log2 Yi ,t − log2 Yj ,t ‘Minus’

At =log2 Yi,t+log2 Yj,t

2 ‘Ave’.

CLN

How do we locally adjust peak intensities?

I Consider a pairwise comparison of two spectra

I Let the first spectra, i , have the intensity Yi ,t at mass t

I Similarly Yj ,t for the second spectra

Now define the values:

Mt = log2 Yi ,t − log2 Yj ,t ‘Minus’

At =log2 Yi,t+log2 Yj,t

2 ‘Ave’.

CLN

How do we locally adjust peak intensities?

I Consider a pairwise comparison of two spectra

I Let the first spectra, i , have the intensity Yi ,t at mass t

I Similarly Yj ,t for the second spectra

Now define the values:

Mt = log2 Yi ,t − log2 Yj ,t ‘Minus’

At =log2 Yi,t+log2 Yj,t

2 ‘Ave’.

This way, ∀t, plot Mt vs At

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●

●

●●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●●

●

●●

●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●●

●

●●

●

●●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●●●●●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●●●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●●

●●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●●●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●

●●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●●●●

●●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●●

●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●●●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●●

●

●

●●

●

●●●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●

●●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●

●

●●●●●●

●

●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●

●

●●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●●

●●

●

●●

●●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●●●

●●

●●

●●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●●●●●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●●●●

●

●●

●

●●●

●●●●●●

●

●●●

●●

●

●●●●●●●●●

●

●●●●●●

●

●●●●

●

●

●●●

●

●

●●

●

●●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●●

●

●

●●●

●●

●

●●

●●

●●●●

●●●●●●●●●

●

●

●

●●●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●●

●●

●●●●●●●●

●●●●●●●●●●●

●●●●●●

●● ●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●

−10 −5 0 5

−10

−5

05

1015

A vs M Plot

A

M

Patient 5 vs Patient 111

We can see if there are any mean differences in (log) ratiointensities for similar sized peaks

Contour plot

−10

−5

0

5

10

15

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●●

●●●

●●●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●●

●

●

●

●●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●●

●●

●

●

●●●

●●

●●

●

●●

●

●

●●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●●

●●●●

●

●

●

●●

●●●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●●

●●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●●●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●●

●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●

●●

●●

●●●●

●

●●●

●●

●

●

●

●●

●

●●

●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●

●

●●●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●●●

●

●●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●●●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●●●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●●

●●●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●●●

●

●

●●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●●●

●

●●●

●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●●

●

●●●●

●

●

●

●

●●

●

●

●

●●●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●●

●●

●

●

●●

●

●

●●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●●

●●

●

●●

●

●●●

●

●●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●●●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●●

●

●●

●●

●●

●●●

●

●

●

●

●

●●●●

●●

●

●

●●

●

●

●●

●

●

●●●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●●

●●●●●

●

●

●

●●

●

●●

●

●●

●

●

●●●

●

●●

●●

●●

●

●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●●

●

●

●

●

●

●●●

●

●

●

●●●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●●●●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●

●

●

●

●●●●●●

●

●

●

●

●

●

●●●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●●●

●●

●●

●

●

●

●●●●●●●

●

●

●●

●●

●●

●

●

●

●

●

●

●●

●●

●

●●

●

●●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●●●

●●

●●

●

●●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●●●●

●

●

●●

●

●●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●●●●

●●●●

●●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●

●●●●

●

●●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●●

●

●

●

●

●●●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●●

●●

●

●

●

●●

●

●

●

●●●●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●●●

●

●●●●●●●●●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●●●

●●●●●●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●●●

●

●●

●●

●

●●●

●

●

●●

●

●●●

●●

●

●

●

●●

●●●

●

●●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●●

●●

●

●

●

●●●

●

●

●

●●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●●

●

●●●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●●●●

●

●

●

●●●

●

●●

●

●

●●●

●

●●●●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●●

●●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●●

●●●

●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●●

●●●

●

●

●●

●

●

●●●

●

●

●●●

●●

●●●

●

●

●●

●

●

●

●●●

●●

●●

●●

●

●●

●

●

●

●

●●●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●●

●

●

●●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●●

●●

●

●●●●●●●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●●

●●

●

●●

●

●●

●

●

●●●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●●

●●●●

●

●●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●●●

●

●

●

●●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●●

●●

●

●

●

●

●

●●●

●

●●●●●

●

●

●

●●●

●

●●

●

●

●

●●●●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●●●

●●●●●●

●

●●

●

●

●

●

●●●

●

●●●

●

●

●●●

●

●

●●

●●●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●●

●●

●

●

●

●

●

●●●

●

●●●●●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●●

●

●

●●●

●

●

●

●●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●●●●

●

●

●●●

●

●

●

●●●

●

●

●●

●●

●

●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●●●●●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●●

●●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●

●●

●●

●●●

●

●●

●

●

●●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●●●●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●●

●

●●●

●

●

●●

●

●●●

●

●

●

●

●

●●●●●

●

●

●

●●

●

●●

●

●●●

●

●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●●●●●

●●●

●

●●

●●●●●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●●●

●●

●●●●●

●●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●

●

●●

●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●●●●●

●●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●●

●

●●

●●●●

●●

●

●

●

●●

●

●●●

●

●

●

●●●●●●

●

●●

●●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●●

●●

●

●●

●●

●

●●●

●

●

●

●●

●

●

●●●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●●●

●●

●●

●

●

●●●●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●

●

●

●●●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●●

●

●●●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●

●●●●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●●●

●●

●

●

●●

●●

●

●

●

●●

●

●

●

●●●

●

●

●●

●●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●●

●●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●●

●●

●

●

●●●●

●●

●

●

●

●

●●●

●

●

●

●●●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●●●●

●●●

●●

●

●

●

●●●

●●

●

●●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●●●●

●

●●●●●

●●

●●●●

●

●

●

●●

●

●●●●

●

●

●

●●●●

●

●

●●●●

●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●●●●●●

●

●

●●

●

●

●

●

●●●

●

●

●●

●●●

●●

●

●

●

●

●●

●

●●

●

●

●●●●●●

●●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●●

●●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●●●

●●

●

●

●●●

●

●

●●●

●

●

●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●●

●

●●●●●●●●●

●

●

●

●●

●

●●

●

●

●

●

●●●●

●●

●

●●

●

●●

●●

●

●●

●

●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●●

●

●●●●●●

●

●●

●

●●●

●

●

●●●●

●

●

●

●

●●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●●

●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●●

●

●●

●●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●

●●●

●

●●●●●

●

●●●

●

●

●●●●

●

●

●●

●

●

●

●●

●●

●●●●

●●

●

●

●

●●

●

●

●

●●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●●●

●●

●

●

●

●●

●

●

●●●●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●●

●●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●●●●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●●●

●●

●

●

●

●

●●

●●

●

●

●●

●

●

●●

●●●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●●

●●

●●●

●

●●

●

●●

●

●

●●●

●

●●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●●

●●●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●●●

●

●

●●

●

●●

●

●

●●●

●

●

●●

●

●

●

●

●

●●●●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●●

●

●●

●●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●●

●●●●●●

●

●●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●●●●

●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●●●

●

●●

●

●●

●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●

●

●●●

●●

●

●●●●●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●●●●●

●

●

●●●

●

●●

●

●

●●

●

●●●

●

●●●

●

●●

●

●●●

●

●●●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●●●●

●

●

●●

●

●

●

●

●

●●

●●●

●●●●

●

●●

●●

●●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●●●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●●

●●●●●●●

●

●

●●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●●

●●

●●

●●●●●

●●●●

●

●

●

●●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●

●●●●●

●

●●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●●●

●

●●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●●●●

●

●●●

●

●

●

●

●

●

●●●●●

●

●●●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●●●

●●

●●●

●

●

●

●

●

●

●

●●●●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●●

●

●●

●

●●●

●●

●

●

●●●

●

●

●

●

●●

●

●●●●●

●●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●●

●

●

●

●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●

●

●●

●

●

●●●●

●

●

●

●

●

●

●

●

●●

●

●●●

●●●

●

●

●●●

●●●●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●●

●●

●

●●●●

●●●

●

●

●

●

●

●

●●

●

●●●●

●

●●●●

●

●

●

●

●●●

●

●●●●●●●

●

●

●

●

●

●●

●

●

●●●●

●●●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●●

●●

●

●●●

●

●

●

●

●

●●

●●

●●

●

●●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●●

●●●

●

●●

●

●●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●●●

●●

●●

●

●●●●

●

●

●●●●●●●●

●

●

●

●

●●

●●

●

●

●●●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●●●●

●

●●●

●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●●

●

●

●

●

●●●

●

●●●

●

●●

●●

●

●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●●

●

●

●

●●●

●

●●●

●

●●●

●

●

●

●●●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●●

●

●●●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●●

●●●●

●●

●

●

●●

●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●●●●

●●

●

●

●●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●●●●

●

●

●

●

●

●

●●●●●

●●

●●

●●

●●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●●

●●●

●

●●●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●

●●●

●

●●

●●

●

●

●●

●●

●

●

●●

●

●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●●●

●●●●

●●

●

●

●

●

●

●

●

●●●●

●

●

●

●●

●

●●

●●

●

●●●●

●

●

●

●

●

●

●

●●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●●●

●

●

●●●

●

●●

●●●●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●●●

●●

●

●●●

●●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●●●

●

●

●

●

●●

●●

●

●●●

●●●●

●●●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●●

●●

●●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●

●

●

●

●

●●

●

●

●●●●

●

●●●●

●●●

●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●●●●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●

●

●●

●

●

●●

●●

●●

●●

●●●●

●

●●●

●

●●●

●●

●

●

●●

●●

●●●●

●

●●

●

●●

●

●

●

●●●●●

●

●

●

●

●

●●

●●

●●

●●●

●●

●

●

●

●●●●

●

●●●

●●●●

●

●●

●

●

●●

●●●●

●●

●●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●●●

●

●●

●●

●●●

●

●●

●●

●

●●●

●●

●

●

●●

●

●●●

●●

●

●●●

●

●

●●●

●●●

●

●●●●●

●

●

●

●●

●

●

●●●

●

●●●●

●●

●

●●●●

●●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●●●●●●

●●●●●●●

●

●●●

●

●

●

●

●●●●●

●

●

●

●

●

●●

●●

●

●●

●

●

●●●

●

●

●●

●●

●●●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●●

●●●

●●

●

●

●

●●●●

●

●

●

●●●

●

●

●

●●●●

●●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●●●

●●●

●

●

●

●●●

●

●●

●

●●●

●

●

●

●●

●

●●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●●●●●

●●

●

●●

●

●

●●●

●

●●●

●

●●

●●

●●

●●

●●●●

●●

●

●

●

●

●

●

●●●

●

●●●●

●

●●●

●

●

●●

●

●

●●

●●

●

●

●●●

●

●

●

●●

●●●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●●

●●●

●

●●

●

●

●●

●

●

●

●●

●

●

●●

●

●●●●

●

●●●●●

●

●●●

●●

●

●●●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●●

●●

●

●●

●

●●●

●

●

●

●●

●●●

●

●●

●●

●

●●●●●

●●●

●

●

●

●●

●●

●

●

●●●●

●

●

●

●

●

●●●

●

●●●

●

●

●

●●

●

●●●●

●●

●●●

●

●●

●●

●

●●●

●

●●

●

●

●

●●

●●

●●

●

●

●

●●●

●

●

●

●

●●

●●●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●●

●

●

●

●●●

●

●

●●

●

●●

●

●●●

●

●●

●

●●

●

●●

●●●

●●

●

●

●

●

●

●

●●●

●●●

●●●●●●

●●

●

●

●●●●●

●

●

●

●

●

●

●●

●

●●

●

●●

●●

●●●●●

●●

●

●

●●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●●●●●●

●

●●●●●●●●●●●●●●●

●

●●●●●●●●●●

●●●●●●●●●●●

●

●●●●●●●●●●●●●

●

●

●●●●●

●

●●●

●

●

●●●●●

●

●●●●●●●●●●●●●●●●●●●●●●●●●

●

●

●●●●

●

●●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●●

●●

●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

−10 −5 0 5A

M

Est density

0.02

0.04

0.06

0.08

Adjusting the intensities

How do we do this?

I Mt ← Mt − f (At)

I Where f is the loess regression function (red line is theprevious slide)

I These adjustments can then be transformed back to theoriginal scale (the spectra)

Adjusting the intensities

How do we do this?

I Mt ← Mt − f (At)

I Where f is the loess regression function (red line is theprevious slide)

I These adjustments can then be transformed back to theoriginal scale (the spectra)

Adjusting the intensities

How do we do this?

I Mt ← Mt − f (At)

I Where f is the loess regression function (red line is theprevious slide)

I These adjustments can then be transformed back to theoriginal scale (the spectra)

Adjusting the intensities

How do we do this?

I Mt ← Mt − f (At)

I Where f is the loess regression function (red line is theprevious slide)

I These adjustments can then be transformed back to theoriginal scale (the spectra)

M vs A LOESS adjustment

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●●

●

●

●●●

●●

●●

●

●●

●

●

●●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●

●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●

●●●

●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●●

●●●●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●●

●●

●

●

●

●●●●●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●●

●●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●●●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●●●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●

●●

●

●●●●●●●●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●●●

●

●●●

●●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●●

●

●

●

●●

●

●

●●

●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●●

●●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●●

●●

●

●●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●●●

●

●

●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●●●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●●●●●

●

●●

●

●

●

●

●●●

●

●●●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●●●●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●●

●

●

●

●●●

●

●

●●

●●

●

●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●●●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●●●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●●●

●

●●

●●●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●●●●

●●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●●●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●

●●

●●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●

●

●

●●●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●

●

●●●●

●●

●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●●●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●●●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●●●●●●●

●

●

●

●●

●

●●

●

●

●

●

●●●●

●●

●

●●

●

●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●●

●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●●●

●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●●

●●●

●

●●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●●●

●

●●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●●●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●●

●●●●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●●

●●●●

●

●●●●

●

●

●

●●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●

●●

●

●

●●

●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●●●

●

●

●

●

●●●

●

●●●●●●●

●

●

●

●

●

●●

●

●

●●●●

●●●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●●

●●

●

●

●●●●●●●●

●

●

●

●

●●

●●

●

●

●●●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●●

●

●

●

●

●

●●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●●●

●

●

●●

●

●●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●●

●●●

●

●●

●

●

●●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●●●

●●

●

●

●●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●●●●

●

●

●

●

●

●

●●●●●

●●

●●

●●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●●

●

●●●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●●●

●

●

●●●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●●●

●

●●●●

●●●

●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●

●

●●

●

●

●●

●●

●●

●●

●●●●

●

●●●

●

●●●

●●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●●

●

●

●●●

●●●●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●●

●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●●

●●

●

●●●

●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●

●●●

●

●●●●

●●

●

●●●●

●●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●●●●●●

●

●●●●●●

●

●

●●

●

●

●

●

●●●●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●●

●●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●

●

●●

●●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●●●●●

●●

●

●●

●

●

●●●

●

●

●●

●

●●

●●

●●

●●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●●●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●●●●

●

●

●●●

●●

●

●●●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●●●

●

●

●

●●

●

●●●

●●

●●●

●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●●●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●●

●

●

●●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●●●

●●●●●●

●●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●●●●●

●●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●●●●

●●

●

●●●●●●●●●●●●●

●●

●

●●●●●●●●●●

●●●●●●●

●●●●

●

●

●●●●●

●●●

●●●●

●

●

●●●●●

●

●●●

●

●

●●●●●

●

●●●●●●●●●●●

●●●●●●●●●●●●●

●

●

●

●●●●

●

●●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●●

●●

●●●●●●●●

●●●●●●●●●●●●●●●●●

●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

−10 −5 0 5

−10

−5

05

1015

A vs M Plot

A

M

Patient 5 vs Patient 111●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●●●

●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●●

●●

●

●

●●●

●●

●●

●

●●

●

●

●●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●●

●

●

●●●●

●

●●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●

●

●●●

●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●●●

●●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●●

●

●●

●

●●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●●

●●●●●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●

●●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●●●●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●●●●●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●●

●●

●

●

●

●●●●●●●

●

●

●●

●●

●●

●

●

●

●

●

●

●●

●●

●

●●

●

●●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●●

●●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●●●

●

●●●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●●

●

●

●

●

●●●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●●

●

●●

●

●●●●●●●●

●

●

●

●

●●

●

●

●●●

●

●●

●

●

●

●

●●●

●

●●●

●●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●●

●

●

●

●●

●

●

●●

●

●

●●●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●

●●

●

●

●

●●

●●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●●

●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●●●

●●

●

●●

●

●●●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●

●

●

●●●●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●●●

●

●

●

●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●●●●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●

●

●

●

●

●●●

●

●●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●●●●●

●

●●

●

●

●

●

●●●

●

●●●

●

●

●

●●

●

●

●●

●

●●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●●●●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●

●

●●●

●

●

●

●●●

●

●

●●

●●

●

●

●●

●●●●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●●

●●

●●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●●●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●●●●●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●●●

●

●●

●●●●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●●●●

●●

●

●●

●

●

●

●●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●●●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●●

●●

●●

●

●

●

●●

●

●●●

●

●

●

●

●●●

●●

●

●●

●●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●●

●

●●

●●

●

●●●

●

●

●

●●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●●

●●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●●

●

●

●●●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●●

●●

●●

●

●●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●●

●

●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●

●

●●●●

●●

●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●

●●●●●●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●●●

●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●●●●●●●●●

●

●

●

●●

●

●●

●

●

●

●

●●●●

●●

●

●●

●

●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●●

●●

●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●●●●●

●

●●

●

●●

●●●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●●

●

●●●●●

●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●●

●●●

●

●●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●●●●

●

●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●●

●

●●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●●●

●

●●

●

●●

●

●●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●●●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●●●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●●

●

●

●●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●●

●●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●●

●●●●●●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●●

●●●●

●

●●●●

●

●

●

●●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●●

●●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●●

●●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●●

●

●

●●●

●

●●

●●

●●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●●

●●

●

●●●●

●●

●

●

●

●

●

●

●

●●

●

●●●●

●

●●●●

●

●

●

●

●●●

●

●●●●●●●

●

●

●

●

●

●●

●

●

●●●●

●●●

●●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●●●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●

●●●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●●●●

●

●

●●●●●●●●

●

●

●

●

●●

●●

●

●

●●●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●

●

●

●

●

●●

●

●

●

●

●●●

●

●●●

●

●

●●

●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●●

●

●

●

●

●

●●

●

●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●●

●●

●

●

●

●

●●●

●

●

●●

●

●●●

●

●

●

●●●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●●●

●

●

●●

●

●

●

●

●

●

●●●●

●

●●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●●

●●●

●

●●

●

●

●●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●●●●

●●

●

●

●●

●●

●

●●

●

●

●●

●

●

●●

●

●●

●

●

●

●●

●

●●●●

●

●

●

●

●

●

●●●●●

●●

●●

●●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●●

●●●

●

●●●

●●●

●

●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●●●●

●

●

●

●

●

●

●●

●●

●

●●

●●

●

●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●●

●

●

●

●●

●

●

●

●●●

●

●

●

●

●●

●

●●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●●

●●

●

●

●

●

●●●

●

●

●●●

●

●●

●●●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●●●●

●

●

●

●

●●

●●

●

●

●●

●●

●

●

●●

●●

●

●●

●

●

●

●●

●

●

●

●●

●

●

●

●●●●

●

●●

●

●

●●

●●

●

●●

●

●

●

●

●

●

●●

●●

●

●

●●●●

●

●

●●

●●●

●

●

●

●●

●●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●●●●

●

●●●●

●●●

●

●●

●

●●

●

●

●●●

●

●●

●

●●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●

●

●

●●●

●

●

●

●●

●●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●●●

●

●

●●

●

●●

●

●

●●

●●

●●

●●

●●●●

●

●●●

●

●●●

●●

●

●

●

●

●●

●●●

●

●

●

●

●

●

●

●

●

●

●●●●●

●

●

●

●

●

●●

●●

●●

●●

●

●●

●

●

●

●●●

●

●

●●●

●●●●

●

●

●

●

●

●●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●

●●

●

●

●

●

●

●●

●●

●●●

●

●●

●●

●

●

●●

●●

●

●

●●

●

●

●●

●●

●

●●●

●

●

●●

●

●●●

●

●●●

●

●

●

●

●

●●

●

●

●●●

●

●●●●

●●

●

●●●●

●●

●●

●●

●

●

●

●

●

●

●

●

●●

●

●

●●●●

●●●●●●

●

●●●●●●

●

●

●●

●

●

●

●

●●●●●

●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●

●

●●

●●

●●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●●

●

●●●

●

●

●

●●

●●

●

●

●

●●●

●

●

●

●

●●●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●●

●

●

●●●●●

●●

●

●●

●

●

●●●

●

●●●

●

●●

●●

●●

●●

●●●●

●●

●

●

●

●

●

●

●●

●

●

●●●●

●

●●

●

●

●

●●

●

●

●●

●

●

●

●

●●●

●

●

●

●

●

●●●●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●●●●

●

●

●●●

●●

●

●●●●●

●

●●

●

●

●

●●

●

●

●

●●

●

●●●

●

●●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●●

●●●

●

●●

●●

●

●●●

●●

●●●

●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●●●

●

●●

●

●

●

●

●

●

●

●●●

●

●●

●●●

●

●●

●●

●

●

●●

●

●●

●

●

●

●●

●●

●●

●

●

●

●

●●

●

●

●

●

●●

●●

●

●●●

●

●

●●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●●

●

●

●●

●

●●

●

●●●

●

●

●

●

●●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●●●

●●●●●●

●●

●

●

●●●●●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●●●●●

●●

●

●

●

●

●

●●

●

●●●●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●●●●●

●●

●

●●●●●●●●●●●●●

●●

●

●●●●●●●●●●

●●●●●●●●●●●

●

●

●●●●●●●●

●●●●

●

●

●●●●●

●

●●●

●

●

●●●●●

●

●●●●●●●●●●●●●●●●●●●●●●●●

●

●

●

●●●●

●

●●

●●●

●●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●●●

●●●●

●●

●●●●●●●●

●●●●●●●●●●●●●●●●●

●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

−10 −5 0 5

−10

−5

05

1015

A vs M Plot

A

M a

djus

ted

Patient 5 vs Patient 111

CLN

One last consideration...

I We want to adjust intensities within the experiment in apairwise fashion

I This requires n(n−1)2 comparisons

I As now we are adjusting each spectra by all others, weaverage the adjustments for each spectra

I Continue iterating process until a threshold of minimumchange is achieved (thus cyclic LOESS)

CLN

One last consideration...

I We want to adjust intensities within the experiment in apairwise fashion

I This requires n(n−1)2 comparisons

I As now we are adjusting each spectra by all others, weaverage the adjustments for each spectra

I Continue iterating process until a threshold of minimumchange is achieved (thus cyclic LOESS)

CLN

One last consideration...

I We want to adjust intensities within the experiment in apairwise fashion

I This requires n(n−1)2 comparisons

I As now we are adjusting each spectra by all others, weaverage the adjustments for each spectra

I Continue iterating process until a threshold of minimumchange is achieved (thus cyclic LOESS)

CLN

One last consideration...

I We want to adjust intensities within the experiment in apairwise fashion

I This requires n(n−1)2 comparisons

I As now we are adjusting each spectra by all others, weaverage the adjustments for each spectra

I Continue iterating process until a threshold of minimumchange is achieved (thus cyclic LOESS)

Results

How can we assess the effectiveness of a normalisation?

I or a pre-processing method?

Theory PracticeUse simulated data Use real MS data

Variability •CV of peaks •CV of peaks•MSE of peak •TIC over subsets

prediction of the m/z axis

Classification •Work in •Compare classification errorprogress with different data handling,

feature selection anddiscrimination methods

Coefficient of variation (CV)

A robust CV has been used in the literature, given by

CVr =

∑ni=1 simi∑ni=1 m2

i

.

For spectra i

I mi is the mean of the peaks

I si is the standard deviation of the peaks

Normalisation methodCVr value TIC CLN

Simulated data 2.16 2.08Real data∗ 2.08 2.02

∗Asthma dataset

Simulated data

Consider P proteins/peptides

Let the presence of each peak p = 1, . . . ,P be governed by

βp ∼ Bernoulli (αp) .

Now define Yp as the realised expression of protein p if it is presentin a spectrum

log2 Yp = Xp ∼ N (µp, σp) .

A starting point might be the total protein ion count (TPIC)defined as

θ = µ = α1µ1 + α2µ2 + . . .+ αPµP .

MSE values using different normalisation methods on the generated data (log2 scale)

Normalisation methodTIC CLN

θ̂ 619.6 619.2

θ 703.0 703.0

MSE 6954.6 7019.5

Var [θ̂] 42.1 42.1

bias(θ̂, θ) 83.1 83.5

Var [X̃i ] 8103.7 3046.4

Density/histogram plots of TIC for Asthma spectra (4000-7000m/z)

(a)0.00000

0.00005

0.00010

0.00015

0 5000 10000 15000 20000TIC

Dens

ity Class

GrpF

GrpM

(b)0e+00

1e−04

2e−04

3e−04

0 5000 10000 15000 20000TIC

Dens

ity Class

GrpF

GrpM

(c)0e+00

2e−04

4e−04

6e−04

0 5000 10000 15000 20000TIC

Dens

ity Class

GrpF

GrpM

(a) No normalisation (b) TIC Normalisation (c) Cyclic LOESS normalisation

Spatial visualisations - TIC of spectra by MALDI chip location - raw vs normalised1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

N

M

L

K

J

I

H

G

F

E

D

C

B

A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

N

M

L

K

J

I

H

G

F

E

D

C

B

A

Log2 TIC units

20.9

22.7

24.5

26.3

Run-order heatmap of spectra - raw data

Conclusions

Not clear whether CLN is the best way to go

I Reduces variability of the signal (peaks and TIC)

I Probably does not increase the classification signal

M vs A visualisations are important as a check for experimentalbias

I We haven’t touched on visualisation of batch-order effects

I Using heatmaps and variability markers in the schematic ofthe MALDI chip

Despite thisI We have created a framework to test a given normalisation

method’s effectivenessI Theory and practice

I Not just for normalisation...

Thank you

A special thank you to Peter Hoffman, Vicki Clifton, Megan Pennoand the team at the Adelaide Proteomics Centre.

ReferencesW. Meuleman et al.Comparison of normalisation methods for surface-enhanced laserdesorption and ionisation (SELDI) time-of-flight (TOF) massspectrometry dataBMC Bioinformatics, 9(1):88, 2008.

J. S. Morris et al.Feature extraction and quantification for mass spectrometry inbiomedical applications using the mean spectrum.Bioinformatics, 21(9):1764-1775, 2005.

K. R. Coombes et al.Improved peak detection and quantification of mass spectrometrydata acquired from SELDI by denoising spectra with theundecimated discrete wavelet transform.Proteomics, 5(16):4107-4117, 2005.

A. C. Sauve and T. P. SpeedNormalization, baseline correction and alignment ofhigh-throughput mass spectrometry data.Proceedings of the Genomic Signal Processing and Statisticsworkshop, 2004.

G. K. Smyth and T. SpeedNormalization of cDNA microarray data.Methods, 31(4):265-273, 2003.

D. EdwardsNon-linear normalization and background correction inone-channel cDNA microarray studies.Bioinformatics, 19(7):825-833, 2002.

M vs A LOESS Normalisation - effect

m/z

Inte

nsity

1400 1600 1800 2000

040

040

Adjusted patient 5Original patient 5

Adjusted patient 111Original patient 111