From 5c2846e8ba8a0a9a56d11a65faed7df1328e96cc Mon Sep 17 00:00:00 2001 From: caes Date: Wed, 30 Mar 2016 12:23:09 -0400 Subject: [PATCH] adding derivations for central potential and hydrogen atom --- lecture_notes/3-25/central potential states | 131 ++ lecture_notes/3-25/hydrogen atom | 1 + lecture_notes/3-25/overview | 65 +- lecture_notes/3-28/.ps | 0 lecture_notes/3-28/3-28-overview.txt | 1 + lecture_notes/3-28/hydrogen atom | 79 +- lecture_notes/3-28/hydrogen atom.ps | 2335 +++++++++++++++++++ 7 files changed, 2549 insertions(+), 63 deletions(-) create mode 100644 lecture_notes/3-25/central potential states create mode 120000 lecture_notes/3-25/hydrogen atom create mode 100644 lecture_notes/3-28/.ps create mode 100644 lecture_notes/3-28/3-28-overview.txt create mode 100644 lecture_notes/3-28/hydrogen atom.ps diff --git a/lecture_notes/3-25/central potential states b/lecture_notes/3-25/central potential states new file mode 100644 index 0000000..b1d0eee --- /dev/null +++ b/lecture_notes/3-25/central potential states @@ -0,0 +1,131 @@ +Bound states of a central potential +━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ + + For any central potential V(r) = V(│r│) the eigenfunctions of H can be + separated as + + ❬r❙E,l,mₗ❭ = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,φ) + + (pic) The radial S.E. is + + ⎡−͟ħ͟²⎛ ∂͟²͟ + 2͟ ∂͟ ⎞ + l͟(l͟+͟1͟)ħ͟² + V(│r│) ⎤ Rₑ﹐ₗ(r) = E Rₑ﹐ₗ(r) + ⎣2m ⎝ ∂r² r ∂r ⎠ 2 m r² ⎦ + + (pic) Developed radial schrodinger equation using U(r) replacement + + Rₑ﹐ₗ(r) = Uₑ﹐ₗ(r) /r + + ⎡−͟ħ͟²⎛ ∂͟²͟ + 2͟ ∂͟ ⎞⎤ U͟ = E ∂͟²͟ U + ⎣2m ⎝ ∂r² r ∂r ⎠⎦ r ∂r² + + ∂͟ U͟ = 1͟ ∂͟ U - U͟ + ∂r r r ∂r r² + + ∂͟²͟ U͟ = 1͟ ∂͟²͟ U + 2͟U͟ - 2͟ ∂͟ U + ∂r² r r ∂r² r³ r²∂r + + ⎡−͟ħ͟²⎛ ∂͟²͟ U͟ + 2͟ ∂͟ U͟ ⎞⎤ = E ∂͟²͟ U + ⎣2m ⎝ ∂r² r r ∂r r ⎠⎦ ∂r² +──────────────────────────────────────────────────────────────────────────────── + ⎡−͟ħ͟²⎛ 1͟ ∂͟²͟ U + 2͟U͟ - 2͟ ∂͟ U + 2͟ 1͟ ∂͟ U - 2͟ U͟ ⎞⎤ + ⎣2m ⎝ r ∂r² r³ r²∂r r r ∂r r r² ⎠⎦ + + = E 1͟ ∂͟²͟ U + E 2͟U͟ - E 2͟ ∂͟U + r ∂r² r³ r²∂r +──────────────────────────────────────────────────────────────────────────────── + ⎡−͟ħ͟²⎛ 1͟ ∂͟²͟ + 2͟ - 2͟ ∂͟ + 2͟ ∂͟ - 2͟ ⎞U⎤ + ⎣2m ⎝ r ∂r² r³ r²∂r r² ∂r r³⎠ ⎦ + + = E ⎛1͟ ∂͟²͟ + 2͟ - 2͟ ∂ ⎞U + ⎝r ∂r² r³ r²∂r⎠ +──────────────────────────────────────────────────────────────────────────────── + ⎡⎛−͟ħ͟² 1͟ ∂͟²͟ + −͟ħ͟² 2͟ - −͟ħ͟² 2͟ ∂͟ + −͟ħ͟² 2͟ ∂͟ - −͟ħ͟² 2͟ ⎞U⎤ + ⎣⎝2m r ∂r² 2m r³ 2m r²∂r 2m r² ∂r 2m r³⎠ ⎦ + + = E ⎛1͟ ∂͟²͟ + 2͟ - 2͟ ∂ ⎞U + ⎝r ∂r² r³ r²∂r⎠ +──────────────────────────────────────────────────────────────────────────────── + ⎡⎛−͟ħ͟² 1͟ ∂͟²͟ - −͟ħ͟² 2͟ ∂͟ + −͟ħ͟² 2͟ ∂͟ + −͟ħ͟² 2͟ - −͟ħ͟² 2͟ ⎞U⎤ + ⎣⎝2m r ∂r² 2m r²∂r 2m r² ∂r 2m r³ 2m r³⎠ ⎦ + + = E ⎛1͟ ∂͟²͟ + 2͟ - 2͟ ∂ ⎞U + ⎝r ∂r² r³ r²∂r⎠ +──────────────────────────────────────────────────────────────────────────────── + ↓ + Not sure this makes sense, but the final result is + ↓ + + ⎡−͟ħ͟²∂͟²͟ - ħ͟² l(l+1) + V(│r│)⎤ Uₑ﹐ₗ(r) = E Uₑ﹐ₗ(r) + ⎣2m ∂r² 2mr² ⎦ + + + Normalization Condition + + ∞ ∞ + ∫ │Rₑ﹐ₗ│² r² dr = ∫ │Uₑ﹐ₗ│² dr + 0 0 + + + If V(r) is not more singular at the origin than 1/r^2 then the SE has power + series solutions. + + Thus for small r we take U(r) → rˢ + + (pic) substitute U(r) = rˢ into S.E. + + Uₑ﹐ₗ(r) ≈ rˢ + + ⎡−͟ħ͟² ∂͟²͟ + ħ͟² l(l+1) + V(│r│)⎤ rˢ = E rˢ + ⎣2m ∂r² 2mr² ⎦ + + −͟ħ͟² s(s-1)∂͟ rˢ⁻² + l͟ (l+1)ħ²rˢ⁻² + V(│r│)rˢ = E rˢ + 2m ∂r 2m + + −͟ħ͟² ⎛s(s-1)∂͟ + l͟ (l+1)ħ²⎞rˢ⁻² + V(│r│)rˢ = E rˢ + 2m ⎝ ∂r 2m ⎠ + + + −͟ħ͟² ⎛s(s-1)∂͟ + l͟ (l+1)ħ²⎞rˢ⁻² + V(│r│)rˢ = E rˢ + 2m ⎝ ∂r 2m ⎠ + + −͟ħ͟² ⎛s(s-1)∂͟ + l͟ (l+1)ħ²⎞ + V(│r│)r² = E r² + 2m ⎝ ∂r 2m ⎠ + + + For r → 0, + r² → 0, + V(r) r² → 0. + ⇓ + s(s-1) + l(l+1) = 0 + ⇓ + s = l+1 or s = -l + + If s = -l, the normalization conditions + + ∞ │∞ + ∫ r⁻²ˡ dr = 1/(2l-1) 1/(r²ˡ⁻¹) │ → diverges + 0 │0 + + + So, for small r, + + Uₑ﹐ₗ(r) → (r→0) → rˡ⁺¹; + + Rₑ﹐ₗ(r) → (r→0) → rˡ. + +Eigenfunctions +━━━━━━━━━━━━━━ + + Ψₑ﹐ₗ﹐ₘ(r,θ,φ) = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,φ) = Uₑ﹐ₗ /r Yₗ﹐ₘ(θ,φ) + + ⇒ d͟²͟ U - 1͟ l(l+1) + ⎛λ͟ - 1͟⎞U = 0 + dρ² ρ² ⎝ρ 4⎠ + + ⎡−͟ħ͟² d² + l͟ (l+1)ħ² - Z͟e͟²⎤Uₑ﹐ₗ(r) = E Uₑ﹐ₗ(r) + ⎣2m dr² 2mr² r ⎦ + + ρ = √⎛8͟m͟ │E│⎞r + ⎝ ħ² ⎠ + + λ = Z͟e͟² √⎛_͟m͟_͟ ⎞ + ħ ⎝2│E│⎠ diff --git a/lecture_notes/3-25/hydrogen atom b/lecture_notes/3-25/hydrogen atom new file mode 120000 index 0000000..7a70ff1 --- /dev/null +++ b/lecture_notes/3-25/hydrogen atom @@ -0,0 +1 @@ +../3-28/hydrogen atom \ No newline at end of file diff --git a/lecture_notes/3-25/overview b/lecture_notes/3-25/overview index 4ac7100..23f6ff7 100644 --- a/lecture_notes/3-25/overview +++ b/lecture_notes/3-25/overview @@ -1,65 +1,10 @@ -Bound states of a central potential -━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ +Computed the bound states of a central potential with eigenfunctions of H + ❬r❙E,l,mₗ❭ = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,ϕ). -For any central potential V(r) = V(│r│) the eigenfunctions of H can be separated as - - ❬r❙E,l,mₗ❭ = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,ϕ) - -The radial S.E. is - - ⎡−͟ħ͟² ⎛ ∂͟²͟ + 2͟∂͟ ⎞ + l͟(l͟+͟1͟)ħ͟² + V(│r│) ⎤ Rₑ﹐ₗ(r) = E Rₑ﹐ₗ(r) - ⎣2m ⎝ ∂r² r∂r ⎠ 2 m r² ⎦ - - - Rₑ﹐ₗ(r) = U͟ₑ͟﹐͟ₗ͟(r) - r - - (pic) ... - -(pic) Developed radial schrodinger equation using U(r) replacement - - - Developed normalization condition - -If V(r) is not more singular at the origin than 1/r^2 then the SE has power series solutions. - - Thus for small r we take U(r) → rˢ - -(pic) substitute U(r) = rˢ into S.E. - - -ħ²/2m [(s(s-1) + l(l+1)] + V r² = E r² - - For r → 0 - r² → 0 - V(r) r² → 0 - - ⇒ s(s-1) + l(l+1) = 0 - ⇒ s = l+1 or s = -l - - If s = -l, the normalization conditions - - ∞ │∞ - ∫ r⁻²ˡ dr = 1/(2l-1) 1/(r²ˡ⁻¹) │ → diverges - 0 │0 - - - Uₑ﹐ₗ(r) → (r→0) → rˡ⁺¹ - - Rₑ﹐ₗ(r) → (r→0) → rˡ - - -The Hydrogen Atom -━━━━━━━━━━━━━━━━━ - - V(r) = -e²/r - - For a hydrogenic ion with nuclear charge Z - - V(r) = -Ze²/r - - Eigenfunctions: - - Ψₑ﹐ₗ﹐ₘ(r,θ,φ) = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,φ) = Uₑ﹐ₗ/r Yₗ﹐ₘ(θ,φ) + (pic) Developed radial schrodinger equation using U(r) replacement + If V(r) is not more singular at the origin than 1/r^2 then the SE has power series solutions. +Began the Hydrogen Atom diff --git a/lecture_notes/3-28/.ps b/lecture_notes/3-28/.ps new file mode 100644 index 0000000..e69de29 diff --git a/lecture_notes/3-28/3-28-overview.txt b/lecture_notes/3-28/3-28-overview.txt new file mode 100644 index 0000000..fdbe063 --- /dev/null +++ b/lecture_notes/3-28/3-28-overview.txt @@ -0,0 +1 @@ +Developed Theory for The Hydrogen Atom diff --git a/lecture_notes/3-28/hydrogen atom b/lecture_notes/3-28/hydrogen atom index 3e8b813..8ca5ece 100644 --- a/lecture_notes/3-28/hydrogen atom +++ b/lecture_notes/3-28/hydrogen atom @@ -1,9 +1,18 @@ Theory of the Hydrogen Atom ━━━━━━━━━━━━━━━━━━━━━━━━━━━━ + V(𝐫) = -e²/r - Derived from first principles the wave equation of an electron in the hydrogen atom. + For any hydrogenic ion with nuclear charge Z + V(𝐫) = -Ze²/r - -Start with Dirac Notation + Eigenfunctions in spherical coordinates: + + Ψₑ﹐ₗ﹐ₘ(r,θ,φ) = Rₑ﹐ₗ(r) Yₗ﹐ₘ(θ,φ) = Uₑ﹐ₗ/r Yₗ﹐ₘ(θ,φ) + + Derived from first principles the wave equation of an electron in the + hydrogen atom. + + - Start with Dirac Notation - Replace with known general functions - transform to eigenvalue equation in position space - replace pieces with function F and find derivatives @@ -15,4 +24,68 @@ Theory of the Hydrogen Atom These are infinite, though, so - Force Laguerre Polynomial solutions to truncate - - \ No newline at end of file +Derivation +━━━━━━━━━━ + The Hydrogen atom follows the central potential development from the + previous lecture. + + ❬r,θ,φ❙Ψ❭ = R(r)ₑ,ₗ yₗ﹐ₘ(θ,φ) + + Rₑ﹐ₗ(r) = Uₑ﹐ₗ(r) /r + + ρ ≡ √⎛8͟m͟ │E│⎞r + ⎝ ħ² ⎠ + + λ = Z͟e͟² √⎛_͟m͟_͟ ⎞ + ħ ⎝2│E│⎠ + + d͟²͟ U - 1͟ l(l+1) + ⎛λ͟ - 1͟⎞U = 0 + dρ² ρ² ⎝ρ 4⎠ + + + as ρ→0, U→ρˡ⁺¹ + + for ρ→∞, + + d͟²͟ U - 1͟U = 0 + dρ² 4 + + d͟²͟ U - 1͟U = 0 + dρ² 4 + + U(ρ) = A exp(-ρ/2) + B exp(ρ/2) = A exp(-ρ/2) + (ρ→∞, B=0) + + U(ρ) = ρˡ⁺¹ exp(-ρ/2) Fₑ﹐ₗ(ρ) + + d͟ U = (l+1)ρˡ exp(-ρ/2) Fₑ﹐ₗ(ρ) + dρ + -½ ρˡ⁺¹ exp(-ρ/2) Fₑ﹐ₗ(ρ) + + + ρˡ⁺¹ exp(-ρ/2) d͟ Fₑ﹐ₗ(ρ) + dρ + + d͟ U = ⎛l͟+͟1͟ - 1͟ ⎞ U + ρˡ⁺¹ exp(-ρ/2) d͟ F(ρ) + dρ ⎝ ρ 2 ⎠ dρ + + + + d͟²͟ U = -(l͟+͟1͟) U + ⎛l͟+͟1͟ - 1͟⎞² U + dρ² ρ² ⎝ ρ 2⎠ + + 2⎛l͟+͟1͟ - 1͟⎞ρˡ⁺¹ exp(-ρ/2) d͟F͟ + ⎝ ρ 2⎠ dρ + + ρˡ⁺¹ exp(-ρ/2) d͟²͟ F(ρ) + dρ² + + + + + ⎡−͟ħ͟² d² + l͟ (l+1)ħ² - Z͟e͟²⎤Uₑ﹐ₗ(r) = E Uₑ﹐ₗ(r) + ⎣2m dr² 2mr² r ⎦ + + ρ = √⎛8͟m͟ │E│⎞r + ⎝ ħ² ⎠ + + ⎛⎞ + ⎝⎠ + diff --git a/lecture_notes/3-28/hydrogen atom.ps b/lecture_notes/3-28/hydrogen atom.ps new file mode 100644 index 0000000..eecd0ec --- /dev/null +++ b/lecture_notes/3-28/hydrogen atom.ps @@ -0,0 +1,2335 @@ +%!PS-Adobe-3.0 +%%Title: yo +%%Creator: paps version 0.6.7 by Dov Grobgeld +%%Pages: (atend) +%%BoundingBox: 0 0 595 841 +%%BeginProlog +%%Orientation: Portrait +/papsdict 1 dict def +papsdict begin + +/inch {72 mul} bind def +/mm {1 inch 25.4 div mul} bind def + +% override setpagedevice if it is not defined +/setpagedevice where { + pop % get rid of its dictionary + /setpagesize { + 3 dict begin + /pageheight exch def + /pagewidth exch def + /orientation 0 def + % Exchange pagewidth and pageheight so that pagewidth is bigger + pagewidth pageheight gt { + pagewidth + /pagewidth pageheight def + /pageheight exch def + /orientation 3 def + } if + 2 dict + dup /PageSize [pagewidth pageheight] put + dup /Orientation orientation put + setpagedevice + end + } def +} +{ + /setpagesize { pop pop } def +} ifelse +/duplex { + statusdict /setduplexmode known + { statusdict begin setduplexmode end } {pop} ifelse +} def +/tumble { + statusdict /settumble known + { statusdict begin settumble end } {pop} ifelse +} def +% Turn the page around +/turnpage { + 90 rotate + 0 pageheight neg translate +} def +% User settings +/pagewidth 595 def +/pageheight 841 def +pagewidth pageheight setpagesize +/column_width 523 def +/bodyheight 755 def +/lmarg 36 def +/ytop 791 def +/do_separation_line true def +/do_landscape false def +/do_tumble true def +/do_duplex true def +% Procedures to translate position to first and second column +/lw 20 def % whatever +/setnumcolumns { + /numcolumns exch def + /firstcolumn { /xpos lmarg def /ypos ytop def} def + /nextcolumn { + do_separation_line { + xpos column_width add gutter_width 2 div add % x start + ytop lw add moveto % y start + 0 bodyheight lw add neg rlineto 0 setlinewidth stroke + } if + /xpos xpos column_width add gutter_width add def + /ypos ytop def + } def +} def + +1 setnumcolumns +/showline { + /y exch def + /s exch def + xpos y moveto + column_width 0 rlineto stroke + xpos y moveto /Helvetica findfont 20 scalefont setfont s show +} def +/paps_bop { % Beginning of page definitions + papsdict begin + gsave + do_landscape {turnpage} if + % ps2pdf gets wrong orientation without this! + /Helvetica findfont setfont 100 100 moveto ( ) show + firstcolumn + end +} def + +/paps_eop { % End of page cleanups + grestore +} def +%%BeginProlog +/papsdict 1 dict def +papsdict begin + +/conicto { + /to_y exch def + /to_x exch def + /conic_cntrl_y exch def + /conic_cntrl_x exch def + currentpoint + /p0_y exch def + /p0_x exch def + /p1_x p0_x conic_cntrl_x p0_x sub 2 3 div mul add def + /p1_y p0_y conic_cntrl_y p0_y sub 2 3 div mul add def + /p2_x p1_x to_x p0_x sub 1 3 div mul add def + /p2_y p1_y to_y p0_y sub 1 3 div mul add def + p1_x p1_y p2_x p2_y to_x to_y curveto +} bind def +/start_ol { gsave } bind def +/end_ol { closepath fill grestore } bind def +/draw_char { fontdict begin gsave 0.001000 dup scale last_x last_y translate load exec end grestore} def +/goto_xy { fontdict begin /last_y exch def /last_x exch def end } def +/goto_x { fontdict begin /last_x exch def end } def +/fwd_x { fontdict begin /last_x exch last_x add def end } def +/c /curveto load def +/x /conicto load def +/l /lineto load def +/m /moveto load def +end +/paps_exec { + 1 dict begin + /ps exch def + /len ps length def + /pos 0 def + + % Loop over all the characters of the string + { + pos len eq {exit} if + + % Get character at pos + /ch ps pos 1 getinterval def + + % check for + + (+) ch eq { + /pos 1 pos add def + /xp ps pos 8 getinterval cvi def + /yp ps pos 8 add 8 getinterval cvi def + /pos 16 pos add def + papsdict begin xp yp goto_xy end + } { + (*) ch eq { + /pos 1 pos add def + /xp ps pos 8 getinterval cvi def + /pos 8 pos add def + papsdict begin xp goto_x end + } { (>) ch eq { + /pos 1 pos add def + /xp ps pos 4 getinterval cvi def + /pos 4 pos add def + papsdict begin xp 2 mul fwd_x end + } { (-) ch eq { + /pos 1 pos add def + /xp ps pos 4 getinterval cvi def + /pos 4 pos add def + papsdict begin xp neg 2 mul fwd_x end + } { + % Must be a 3 char sym. Load and exec + /name ps pos 3 getinterval def + papsdict begin name draw_char end + /pos 3 pos add def + } ifelse + } ifelse + } ifelse + } ifelse + } loop + end +} def +/fontdict 1 dict def +papsdict begin fontdict begin +/AAA { start_ol +4464 0 m +2736 0 l +2736 7272 l +504 7272 l +504 8784 l +6696 8784 l +6696 7272 l +4464 7272 l +4464 0 l +7200 fwd_x +end_ol + } def +/BAA { start_ol +936 2336 m +936 6552 l +2664 6552 l +2664 2596 l +2664 1896 2857 1596 x +3052 1296 3504 1296 x +3955 1296 4209 1699 x +4464 2104 4464 2833 x +4464 6552 l +6192 6552 l +6192 0 l +4464 0 l +4464 1019 l +4284 464 3852 159 x +3420 -144 2810 -144 x +1882 -144 1408 481 x +936 1108 936 2336 x +7200 fwd_x +end_ol + } def +/CAA { start_ol +6480 360 m +5883 108 5263 -18 x +4644 -144 3954 -144 x +2311 -144 1443 731 x +576 1606 576 3252 x +576 4846 1413 5771 x +2251 6696 3697 6696 x +5157 6696 5962 5823 x +6768 4950 6768 3364 x +6768 2664 l +2304 2664 l +2309 1938 2760 1580 x +3213 1224 4110 1224 x +4702 1224 5277 1396 x +5852 1569 6480 1944 x +6480 360 l +5040 3960 m +5028 4635 4695 4981 x +4363 5328 3717 5328 x +3133 5328 2786 4970 x +2440 4612 2376 3954 x +5040 3960 l +7200 fwd_x +end_ol + } def +/EAA { start_ol +504 8784 m +2577 8784 l +3596 4911 l +4611 8784 l +6696 8784 l +6696 0 l +5184 0 l +5184 7027 l +4278 3168 l +2932 3168 l +2016 7027 l +2016 0 l +504 0 l +504 8784 l +7200 fwd_x +end_ol + } def +/FAA { start_ol +4127 3096 m +3150 3096 2763 2855 x +2376 2614 2376 2030 x +2376 1595 2643 1337 x +2911 1080 3370 1080 x +4061 1080 4442 1580 x +4824 2082 4824 2981 x +4824 3096 l +4127 3096 l +6552 3751 m +6552 0 l +4824 0 l +4824 776 l +4512 334 4024 94 x +3537 -144 2949 -144 x +1827 -144 1201 444 x +576 1032 576 2088 x +576 3229 1317 3774 x +2059 4320 3614 4320 x +4824 4320 l +4824 4621 l +4824 5005 4516 5202 x +4210 5400 3614 5400 x +3000 5400 2424 5262 x +1849 5125 1224 4824 x +1224 6264 l +1791 6485 2374 6590 x +2959 6696 3614 6696 x +5238 6696 5895 6052 x +6552 5409 6552 3751 x +7200 fwd_x +end_ol + } def +/GAA { start_ol +6768 4680 m +6487 4968 6111 5112 x +5734 5256 5284 5256 x +4740 5256 4334 5062 x +3929 4869 3706 4501 x +3567 4275 3511 3953 x +3456 3632 3456 2977 x +3456 0 l +1728 0 l +1728 6552 l +3456 6552 l +3456 5521 l +3706 6082 4226 6388 x +4746 6696 5441 6696 x +5792 6696 6127 6603 x +6464 6512 6768 6336 x +6768 4680 l +7200 fwd_x +end_ol + } def +/HAA { start_ol +2543 1512 m +6203 1512 l +6203 0 l +648 0 l +648 1465 l +1591 2466 l +3272 4248 3632 4659 x +4074 5166 4269 5556 x +4464 5947 4464 6330 x +4464 6918 4109 7239 x +3755 7560 3106 7560 x +2643 7560 2066 7375 x +1490 7191 864 6840 x +864 8424 l +1487 8669 2084 8798 x +2683 8928 3231 8928 x +4612 8928 5402 8277 x +6192 7627 6192 6503 x +6192 5985 6019 5531 x +5848 5078 5429 4525 x +5121 4125 3736 2724 x +2985 1965 2543 1512 x +7200 fwd_x +end_ol + } def +/IAA { start_ol +1224 216 m +1224 1800 l +1680 1505 2100 1364 x +2520 1224 2908 1224 x +3828 1224 4311 1847 x +4794 2470 4824 3710 x +4549 3331 4122 3141 x +3695 2952 3110 2952 x +1935 2952 1291 3703 x +648 4456 648 5836 x +648 7311 1371 8119 x +2095 8928 3420 8928 x +5026 8928 5753 7857 x +6480 6786 6480 4397 x +6480 2127 5596 991 x +4714 -144 2948 -144 x +2539 -144 2103 -51 x +1668 39 1224 216 x +3465 4392 m +4018 4392 4313 4808 x +4608 5224 4608 6015 x +4608 6799 4313 7215 x +4018 7632 3465 7632 x +2904 7632 2604 7215 x +2304 6799 2304 6015 x +2304 5230 2604 4810 x +2904 4392 3465 4392 x +7200 fwd_x +end_ol + } def +/JAA { start_ol +1080 1512 m +3024 1512 l +3024 7200 l +1224 6768 l +1224 8352 l +3021 8784 l +4680 8784 l +4680 1512 l +6624 1512 l +6624 0 l +1080 0 l +1080 1512 l +7200 fwd_x +end_ol + } def +/KAA { start_ol +792 8784 m +6336 8784 l +6336 7554 l +3355 0 l +1584 0 l +4446 7272 l +792 7272 l +792 8784 l +7200 fwd_x +end_ol + } def +/LAA { start_ol +2664 6264 m +4608 6264 l +4608 4104 l +2664 4104 l +2664 6264 l +2664 2160 m +4608 2160 l +4608 0 l +2664 0 l +2664 2160 l +7200 fwd_x +end_ol + } def +/MAA { start_ol +4104 6854 m +1857 3384 l +4104 3384 l +4104 6854 l +3929 8784 m +5760 8784 l +5760 3384 l +6696 3384 l +6696 1872 l +5760 1872 l +5760 0 l +4104 0 l +4104 1872 l +576 1872 l +576 3560 l +3929 8784 l +7200 fwd_x +end_ol + } def +/NAA { start_ol +3240 3960 m +2304 3960 l +2304 5472 l +3240 5472 l +3891 5472 4249 5728 x +4608 5985 4608 6450 x +4608 6940 4249 7213 x +3891 7488 3240 7488 x +2745 7488 2179 7358 x +1614 7230 1008 6984 x +1008 8568 l +1613 8742 2200 8834 x +2787 8928 3327 8928 x +4713 8928 5488 8327 x +6264 7726 6264 6670 x +6264 5893 5821 5401 x +5380 4908 4560 4756 x +5496 4592 5988 4007 x +6480 3422 6480 2470 x +6480 1195 5658 525 x +4837 -144 3272 -144 x +2604 -144 1957 -32 x +1310 77 720 288 x +720 1872 l +1278 1625 1923 1496 x +2570 1368 3281 1368 x +3993 1368 4408 1690 x +4824 2014 4824 2561 x +4824 3232 4410 3595 x +3996 3960 3240 3960 x +7200 fwd_x +end_ol + } def +/OAA { start_ol +2880 4388 m +2880 4695 3088 4903 x +3296 5112 3596 5112 x +3903 5112 4111 4903 x +4320 4695 4320 4388 x +4320 4088 4111 3880 x +3903 3672 3596 3672 x +3296 3672 3088 3876 x +2880 4082 2880 4388 x +3596 7488 m +2999 7488 2723 6750 x +2448 6012 2448 4388 x +2448 2772 2723 2034 x +2999 1296 3596 1296 x +4200 1296 4476 2034 x +4752 2772 4752 4388 x +4752 6012 4476 6750 x +4200 7488 3596 7488 x +720 4388 m +720 6661 1437 7794 x +2155 8928 3596 8928 x +5044 8928 5762 7797 x +6480 6666 6480 4388 x +6480 2116 5762 985 x +5044 -144 3596 -144 x +2155 -144 1437 988 x +720 2122 720 4388 x +7200 fwd_x +end_ol + } def +/PAA { start_ol +3810 4464 m +3251 4464 2957 4047 x +2664 3631 2664 2840 x +2664 2056 2957 1640 x +3251 1224 3810 1224 x +4368 1224 4667 1640 x +4968 2056 4968 2840 x +4968 3625 4667 4044 x +4368 4464 3810 4464 x +6048 8568 m +6048 6984 l +5591 7272 5171 7416 x +4752 7560 4363 7560 x +3438 7560 2954 6933 x +2471 6306 2448 5081 x +2722 5456 3148 5644 x +3576 5832 4155 5832 x +5337 5832 5980 5081 x +6624 4332 6624 2955 x +6624 1479 5897 667 x +5170 -144 3852 -144 x +2245 -144 1518 927 x +792 1999 792 4388 x +792 6661 1674 7794 x +2557 8928 4323 8928 x +4732 8928 5168 8838 x +5603 8748 6048 8568 x +7200 fwd_x +end_ol + } def +/QAA { start_ol +4199 -752 m +3855 -1674 3373 -2097 x +2892 -2520 2203 -2520 x +792 -2520 l +792 -1224 l +1486 -1224 l +2011 -1224 2255 -1038 x +2500 -852 2751 -176 x +2881 174 l +360 6552 l +2192 6552 l +3685 2299 l +5115 6552 l +6912 6552 l +4199 -752 l +7200 fwd_x +end_ol + } def +/RAA { start_ol +3632 5328 m +3012 5328 2658 4785 x +2304 4243 2304 3276 x +2304 2308 2658 1766 x +3012 1224 3632 1224 x +4259 1224 4613 1766 x +4968 2308 4968 3276 x +4968 4243 4613 4785 x +4259 5328 3632 5328 x +576 3276 m +576 4852 1405 5773 x +2234 6696 3632 6696 x +5037 6696 5866 5773 x +6696 4852 6696 3276 x +6696 1699 5866 777 x +5037 -144 3632 -144 x +2234 -144 1405 777 x +576 1699 576 3276 x +7200 fwd_x +end_ol + } def +/SAA { start_ol +2664 7344 m +2664 4752 l +3369 4752 l +4214 4752 4555 5042 x +4896 5332 4896 6048 x +4896 6763 4555 7053 x +4214 7344 3369 7344 x +2664 7344 l +936 8784 m +3305 8784 l +5112 8784 5904 8139 x +6696 7494 6696 6048 x +6696 4601 5904 3956 x +5112 3312 3305 3312 x +2664 3312 l +2664 0 l +936 0 l +936 8784 l +7200 fwd_x +end_ol + } def +/TAA { start_ol +4680 3351 m +4680 4214 4351 4735 x +4023 5256 3486 5256 x +2955 5256 2629 4737 x +2304 4219 2304 3351 x +2304 2476 2629 1957 x +2955 1440 3486 1440 x +4023 1440 4351 1960 x +4680 2481 4680 3351 x +6408 484 m +6408 -1105 5702 -1812 x +4998 -2520 3414 -2520 x +2880 -2520 2358 -2449 x +1836 -2378 1296 -2232 x +1296 -648 l +1774 -905 2268 -1028 x +2763 -1152 3287 -1152 x +4000 -1152 4340 -802 x +4680 -452 4680 290 x +4680 1003 l +4429 532 4016 301 x +3603 72 3009 72 x +1891 72 1233 947 x +576 1822 576 3323 x +576 4874 1233 5784 x +1891 6696 2998 6696 x +3556 6696 3992 6428 x +4429 6160 4680 5673 x +4680 6552 l +6408 6552 l +6408 484 l +7200 fwd_x +end_ol + } def +/UAA { start_ol +2559 327 m +3361 327 l +3567 327 3567 167 x +3567 0 3360 0 x +1431 0 l +1224 0 1224 167 x +1224 327 1429 327 x +2232 327 l +2232 4208 l +903 4208 l +903 3624 l +903 3408 735 3408 x +576 3408 576 3624 x +576 4536 l +4215 4536 l +4215 3624 l +4215 3408 4055 3408 x +3983 3408 3935 3468 x +3888 3529 3888 3624 x +3888 4208 l +2559 4208 l +2559 327 l +4824 fwd_x +end_ol + } def +/VAA { start_ol +3456 2284 m +3456 2641 3190 2866 x +2926 3092 2497 3092 x +2170 3092 1955 2962 x +1740 2831 1420 2451 x +1335 2347 l +1335 327 l +1690 327 l +1911 327 1911 167 x +1911 0 1689 0 x +645 0 l +432 0 432 167 x +432 327 644 327 x +1008 327 l +1008 4536 l +624 4536 l +432 4536 432 4703 x +432 4863 632 4863 x +1335 4863 l +1335 2751 l +1631 3117 1903 3268 x +2176 3420 2535 3420 x +3084 3420 3433 3106 x +3783 2793 3783 2309 x +3783 327 l +4138 327 l +4359 327 4359 167 x +4359 0 4147 0 x +3156 0 l +2952 0 2952 167 x +2952 327 3141 327 x +3456 327 l +3456 2284 l +4824 fwd_x +end_ol + } def +/WAA { start_ol +4155 1584 m +831 1584 l +919 948 1357 565 x +1797 183 2445 183 x +2821 183 3213 303 x +3604 424 3844 617 x +3924 673 3972 673 x +4036 673 4080 625 x +4124 577 4124 513 x +4124 304 3552 79 x +2981 -144 2437 -144 x +1630 -144 1066 401 x +504 948 504 1728 x +504 2448 1030 2934 x +1558 3420 2325 3420 x +3133 3420 3643 2917 x +4155 2415 4155 1584 x +831 1911 m +3820 1911 l +3723 2446 3316 2769 x +2909 3092 2325 3092 x +1742 3092 1342 2773 x +942 2454 831 1911 x +4824 fwd_x +end_ol + } def +/XAA { start_ol +2396 3420 m +3162 3420 3688 2896 x +4215 2374 4215 1617 x +4215 884 3681 370 x +3146 -144 2396 -144 x +1638 -144 1107 374 x +576 893 576 1642 x +576 2376 1107 2898 x +1638 3420 2396 3420 x +2395 3092 m +1773 3092 1337 2669 x +903 2247 903 1641 x +903 1036 1337 609 x +1773 183 2395 183 x +3010 183 3449 605 x +3888 1028 3888 1617 x +3888 2247 3457 2669 x +3026 3092 2395 3092 x +4824 fwd_x +end_ol + } def +/YAA { start_ol +4156 2730 m +4117 2730 3909 2893 x +3701 3056 3502 3056 x +3229 3056 2937 2867 x +2646 2678 1983 2080 x +1983 327 l +3359 327 l +3567 327 3567 159 x +3567 0 3359 0 x +928 0 l +720 0 720 167 x +720 327 925 327 x +1656 327 l +1656 2984 l +1073 2984 l +864 2984 864 3147 x +864 3312 1075 3312 x +1983 3312 l +1983 2500 l +2534 2998 2877 3190 x +3222 3384 3525 3384 x +3845 3384 4084 3195 x +4324 3007 4324 2896 x +4324 2826 4276 2777 x +4228 2730 4156 2730 x +4824 fwd_x +end_ol + } def +/ZAA { start_ol +2253 -24 m +751 2984 l +623 2984 l +407 2984 407 3152 x +407 3312 623 3312 x +1542 3312 l +1758 3312 1758 3152 x +1758 2984 1542 2984 x +1127 2984 l +2437 336 l +3723 2984 l +3292 2984 l +3076 2984 3076 3152 x +3076 3312 3292 3312 x +4171 3312 l +4387 3312 4387 3152 x +4387 2984 4171 2984 x +4060 2984 l +2013 -1184 l +2533 -1184 l +2749 -1184 2749 -1344 x +2749 -1512 2533 -1512 x +671 -1512 l +455 -1512 455 -1344 x +455 -1184 671 -1184 x +1686 -1184 l +2253 -24 l +4824 fwd_x +end_ol + } def +/bAA { start_ol +4125 4464 m +4109 4464 3931 4482 x +3754 4500 3502 4518 x +3251 4536 3057 4536 x +2678 4536 2439 4339 x +2199 4142 2199 3823 x +2199 3312 l +3648 3312 l +3855 3312 3855 3152 x +3855 2984 3648 2984 x +2199 2984 l +2199 327 l +3575 327 l +3783 327 3783 167 x +3783 0 3576 0 x +1143 0 l +936 0 936 167 x +936 327 1138 327 x +1872 327 l +1872 2984 l +1210 2984 l +1008 2984 1008 3152 x +1008 3312 1210 3312 x +1872 3312 l +1872 3818 l +1872 4273 2209 4568 x +2548 4863 3067 4863 x +3611 4863 4147 4765 x +4287 4727 4287 4614 x +4287 4464 4125 4464 x +4824 fwd_x +end_ol + } def +/cAA { start_ol +1479 3312 m +3210 3312 l +3423 3312 3423 3152 x +3423 2984 3210 2984 x +1479 2984 l +1479 853 l +1479 550 1719 366 x +1959 183 2374 183 x +2710 183 3089 274 x +3469 366 3701 501 x +3781 550 3829 550 x +3885 550 3933 501 x +3981 454 3981 390 x +3981 214 3441 34 x +2902 -144 2390 -144 x +1823 -144 1487 122 x +1152 390 1152 838 x +1152 2984 l +577 2984 l +360 2984 360 3152 x +360 3312 577 3312 x +1152 3312 l +1152 4309 l +1152 4536 1319 4536 x +1479 4536 1479 4309 x +1479 3312 l +4824 fwd_x +end_ol + } def +/dAA { start_ol +3456 2160 m +1335 2160 l +1335 327 l +1719 327 l +1911 327 1911 167 x +1911 0 1706 0 x +644 0 l +432 0 432 167 x +432 327 652 327 x +1008 327 l +1008 4208 l +834 4208 l +648 4208 648 4376 x +648 4536 843 4536 x +1715 4536 l +1911 4536 1911 4376 x +1911 4208 1719 4208 x +1335 4208 l +1335 2487 l +3456 2487 l +3456 4208 l +3072 4208 l +2880 4208 2880 4376 x +2880 4536 3075 4536 x +3947 4536 l +4143 4536 4143 4376 x +4143 4208 3956 4208 x +3783 4208 l +3783 327 l +4146 327 l +4359 327 4359 167 x +4359 0 4154 0 x +3084 0 l +2880 0 2880 167 x +2880 327 3072 327 x +3456 327 l +3456 2160 l +4824 fwd_x +end_ol + } def +/eAA { start_ol +3999 4863 m +3999 327 l +4383 327 l +4575 327 4575 154 x +4575 0 4375 0 x +3672 0 l +3672 707 l +3107 -144 2224 -144 x +1515 -144 1009 388 x +504 921 504 1650 x +504 2379 1009 2899 x +1515 3420 2224 3420 x +3099 3420 3672 2593 x +3672 4536 l +3288 4536 l +3096 4536 3096 4703 x +3096 4863 3296 4863 x +3999 4863 l +2247 3092 m +1659 3092 1245 2671 x +831 2252 831 1650 x +831 1032 1245 607 x +1659 183 2255 183 x +2844 183 3258 607 x +3672 1032 3672 1634 x +3672 2252 3261 2671 x +2851 3092 2247 3092 x +4824 fwd_x +end_ol + } def +/fAA { start_ol +3528 2650 m +3528 3312 l +4231 3312 l +4431 3312 4431 3150 x +4431 2984 4239 2984 x +3855 2984 l +3855 -247 l +3855 -759 3476 -1135 x +3097 -1512 2552 -1512 x +1652 -1512 l +1440 -1512 1440 -1344 x +1440 -1184 1652 -1184 x +2567 -1184 l +2968 -1184 3247 -894 x +3528 -605 3528 -193 x +3528 844 l +2998 72 2155 72 x +1473 72 988 565 x +504 1059 504 1751 x +504 2443 988 2931 x +1473 3420 2155 3420 x +3006 3420 3528 2650 x +2179 3092 m +1617 3092 1224 2704 x +831 2316 831 1751 x +831 1186 1224 793 x +1617 399 2179 399 x +2741 399 3134 788 x +3528 1179 3528 1735 x +3528 2315 3138 2703 x +2749 3092 2179 3092 x +4824 fwd_x +end_ol + } def +/gAA { start_ol +2560 3092 m +2415 3092 2282 3064 x +2149 3037 2032 2977 x +1915 2919 1834 2867 x +1755 2815 1661 2721 x +1569 2626 1532 2583 x +1496 2540 1419 2441 x +1343 2342 1335 2334 x +1335 327 l +1650 327 l +1839 327 1839 167 x +1839 0 1634 0 x +643 0 l +432 0 432 167 x +432 327 652 327 x +1008 327 l +1008 2984 l +726 2984 l +504 2984 504 3150 x +504 3312 724 3312 x +1335 3312 l +1335 2763 l +1681 3143 1947 3281 x +2214 3420 2593 3420 x +3132 3420 3493 3110 x +3855 2801 3855 2341 x +3855 327 l +4096 327 l +4287 327 4287 167 x +4287 0 4090 0 x +3292 0 l +3096 0 3096 167 x +3096 327 3287 327 x +3528 327 l +3528 2284 l +3528 2624 3265 2858 x +3003 3092 2560 3092 x +4824 fwd_x +end_ol + } def +/hAA { start_ol +3421 1544 m +1294 1544 l +862 327 l +1494 327 l +1710 327 1710 167 x +1710 0 1494 0 x +288 0 l +72 0 72 167 x +72 327 288 327 x +535 327 l +1966 4208 l +1006 4208 l +790 4208 790 4376 x +790 4536 1006 4536 x +2637 4536 l +4212 327 l +4507 327 l +4722 327 4722 167 x +4722 0 4507 0 x +3260 0 l +3045 0 3045 167 x +3045 327 3260 327 x +3867 327 l +3421 1544 l +3300 1872 m +2405 4208 l +2286 4208 l +1423 1872 l +3300 1872 l +4824 fwd_x +end_ol + } def +/iAA { start_ol +903 3312 m +903 2896 l +1099 3182 1285 3300 x +1473 3420 1723 3420 x +2232 3420 2494 2857 x +2940 3420 3411 3420 x +3769 3420 4028 3165 x +4287 2912 4287 2563 x +4287 327 l +4555 327 l +4767 327 4767 167 x +4767 0 4551 0 x +3960 0 l +3960 2530 l +3960 2751 3791 2921 x +3622 3092 3403 3092 x +2997 3092 2559 2445 x +2559 327 l +2827 327 l +3039 327 3039 167 x +3039 0 2823 0 x +2232 0 l +2232 2505 l +2232 2736 2079 2913 x +1927 3092 1723 3092 x +1333 3092 903 2445 x +903 327 l +1144 327 l +1335 327 1335 167 x +1335 0 1125 0 x +274 0 l +72 0 72 167 x +72 327 294 327 x +576 327 l +576 2984 l +294 2984 l +72 2984 72 3150 x +72 3312 294 3312 x +903 3312 l +4824 fwd_x +end_ol + } def +/jAA { start_ol +0 2727 m +4794 2727 l +4794 2088 l +0 2088 l +0 2727 l +4824 fwd_x +end_ol + } def +/kAA { start_ol +864 327 m +864 4208 l +623 4208 l +432 4208 432 4376 x +432 4536 642 4536 x +2353 4536 l +3108 4536 3625 3943 x +4143 3351 4143 2497 x +4143 2046 l +4143 1184 3625 591 x +3108 0 2353 0 x +642 0 l +432 0 432 167 x +432 327 623 327 x +864 327 l +3816 2562 m +3816 2723 3745 2965 x +3674 3208 3521 3502 x +3368 3796 3049 4002 x +2731 4208 2315 4208 x +1191 4208 l +1191 327 l +2370 327 l +2936 327 3376 826 x +3816 1327 3816 1973 x +3816 2562 l +4824 fwd_x +end_ol + } def +/lAA { start_ol +2559 3312 m +2559 327 l +3784 327 l +3999 327 3999 167 x +3999 0 3783 0 x +1000 0 l +792 0 792 167 x +792 327 1000 327 x +2232 327 l +2232 2984 l +1353 2984 l +1152 2984 1152 3152 x +1152 3312 1356 3312 x +2559 3312 l +2543 5007 m +2543 4176 l +2088 4176 l +2088 5007 l +2543 5007 l +4824 fwd_x +end_ol + } def +/mAA { start_ol +2685 0 m +2126 0 l +783 2984 l +455 2984 l +239 2984 239 3152 x +239 3312 455 3312 x +1662 3312 l +1886 3312 1886 3152 x +1886 2984 1662 2984 x +1143 2984 l +2341 327 l +2493 327 l +3668 2984 l +3125 2984 l +2909 2984 2909 3152 x +2909 3312 3125 3312 x +4339 3312 l +4555 3312 4555 3152 x +4555 2984 4339 2984 x +4011 2984 l +2685 0 l +4824 fwd_x +end_ol + } def +/nAA { start_ol +3600 928 m +3600 1227 3334 1389 x +3069 1551 2685 1611 x +2301 1670 1918 1730 x +1534 1789 1235 1983 x +936 2178 936 2518 x +936 2909 1326 3164 x +1717 3420 2314 3420 x +3022 3420 3456 3053 x +3456 3085 l +3456 3312 3609 3312 x +3783 3312 3783 3088 x +3783 2535 l +3783 2319 3609 2319 x +3477 2319 3456 2503 x +3422 2774 3121 2932 x +2822 3092 2346 3092 x +1879 3092 1571 2923 x +1263 2756 1263 2505 x +1263 2270 1578 2144 x +1894 2019 2275 1955 x +2658 1892 3043 1828 x +3429 1765 3677 1532 x +3927 1300 3927 909 x +3927 454 3484 155 x +3042 -144 2363 -144 x +1603 -144 1119 286 x +1119 203 l +1119 0 936 0 x +792 0 792 212 x +792 864 l +792 1076 936 1076 x +1119 1076 1119 901 x +1119 844 l +1119 573 1476 378 x +1832 183 2338 183 x +2878 183 3238 393 x +3600 604 3600 928 x +4824 fwd_x +end_ol + } def +/oAA { start_ol +1119 3312 m +1119 2658 l +1446 3071 1782 3245 x +2117 3420 2584 3420 x +3341 3420 3849 2939 x +4359 2459 4359 1751 x +4359 1044 3846 558 x +3333 72 2584 72 x +1667 72 1119 837 x +1119 -1184 l +1852 -1184 l +2055 -1184 2055 -1344 x +2055 -1512 1854 -1512 x +417 -1512 l +216 -1512 216 -1344 x +216 -1184 408 -1184 x +792 -1184 l +792 2984 l +408 2984 l +216 2984 216 3150 x +216 3312 416 3312 x +1119 3312 l +2576 3092 m +1969 3092 1544 2700 x +1119 2307 1119 1751 x +1119 1186 1544 793 x +1969 399 2575 399 x +3181 399 3606 788 x +4032 1179 4032 1735 x +4032 2315 3614 2703 x +3197 3092 2576 3092 x +4824 fwd_x +end_ol + } def +/pAA { start_ol +4263 680 m +4263 609 4127 478 x +3991 347 3771 204 x +3550 61 3189 -40 x +2829 -144 2452 -144 x +1666 -144 1156 349 x +648 844 648 1609 x +648 2399 1168 2909 x +1689 3420 2491 3420 x +3238 3420 3744 2981 x +3744 3085 l +3744 3312 3911 3312 x +4071 3312 4071 3088 x +4071 2360 l +4071 2144 3911 2144 x +3767 2144 3744 2335 x +3720 2653 3346 2873 x +2973 3092 2468 3092 x +1802 3092 1388 2682 x +975 2271 975 1617 x +975 988 1392 586 x +1810 183 2468 183 x +3342 183 3967 752 x +4047 831 4110 831 x +4174 831 4218 787 x +4263 743 4263 680 x +4824 fwd_x +end_ol + } def +/qAA { start_ol +2559 4863 m +2559 327 l +3784 327 l +3999 327 3999 167 x +3999 0 3783 0 x +1000 0 l +792 0 792 167 x +792 327 1000 327 x +2232 327 l +2232 4536 l +1354 4536 l +1152 4536 1152 4703 x +1152 4863 1357 4863 x +2559 4863 l +4824 fwd_x +end_ol + } def +/rAA { start_ol +3524 0 m +3126 0 l +2399 2055 l +1690 0 l +1283 0 l +607 2984 l +455 2984 l +239 2984 239 3152 x +239 3312 455 3312 x +1342 3312 l +1558 3312 1558 3152 x +1558 2984 1342 2984 x +919 2984 l +1494 447 l +2184 2468 l +2594 2468 l +3309 445 l +3852 2984 l +3452 2984 l +3236 2984 3236 3152 x +3236 3312 3452 3312 x +4315 3312 l +4531 3312 4531 3152 x +4531 2984 4315 2984 x +4163 2984 l +3524 0 l +4824 fwd_x +end_ol + } def +/sAA { start_ol +1000 3025 m +1000 3189 1551 3304 x +2102 3420 2410 3420 x +2976 3420 3343 3142 x +3711 2865 3711 2444 x +3711 327 l +4095 327 l +4287 327 4287 154 x +4287 0 4087 0 x +3384 0 l +3384 534 l +2662 -144 1836 -144 x +1270 -144 922 142 x +576 430 576 892 x +576 1409 1048 1732 x +1522 2055 2281 2055 x +2759 2055 3384 1887 x +3384 2446 l +3384 2738 3108 2914 x +2832 3092 2386 3092 x +2013 3092 1616 2984 x +1219 2876 1154 2876 x +1089 2876 1044 2920 x +1000 2965 1000 3025 x +3384 892 m +3384 1608 l +2898 1728 2346 1728 x +1705 1728 1303 1492 x +903 1258 903 884 x +903 565 1154 374 x +1406 183 1827 183 x +2256 183 2617 346 x +2979 509 3384 892 x +4824 fwd_x +end_ol + } def +/tAA { start_ol +3672 2658 m +3672 3312 l +4375 3312 l +4575 3312 4575 3150 x +4575 2984 4383 2984 x +3999 2984 l +3999 -1184 l +4383 -1184 l +4575 -1184 4575 -1344 x +4575 -1512 4374 -1512 x +2937 -1512 l +2736 -1512 2736 -1344 x +2736 -1184 2938 -1184 x +3672 -1184 l +3672 837 l +3138 72 2239 72 x +1507 72 1005 558 x +504 1044 504 1751 x +504 2459 1005 2939 x +1507 3420 2247 3420 x +3130 3420 3672 2658 x +2247 3092 m +1651 3092 1240 2704 x +831 2316 831 1751 x +831 1186 1240 793 x +1651 399 2247 399 x +2836 399 3253 788 x +3672 1179 3672 1735 x +3672 2315 3261 2703 x +2851 3092 2247 3092 x +4824 fwd_x +end_ol + } def +/uAA { start_ol +3528 0 m +3528 525 l +2855 -144 2071 -144 x +1591 -144 1299 142 x +1008 430 1008 901 x +1008 2984 l +624 2984 l +432 2984 432 3152 x +432 3312 632 3312 x +1335 3312 l +1335 901 l +1335 598 1546 390 x +1759 183 2063 183 x +2864 183 3528 914 x +3528 2984 l +2953 2984 l +2736 2984 2736 3152 x +2736 3312 2955 3312 x +3855 3312 l +3855 327 l +4127 327 l +4343 327 4343 154 x +4343 0 4127 0 x +3528 0 l +4824 fwd_x +end_ol + } def +/vAA { start_ol +2351 939 m +2431 939 l +2662 939 2822 790 x +2982 643 2982 419 x +2982 195 2822 43 x +2662 -108 2431 -108 x +2351 -108 l +2119 -108 1959 43 x +1800 195 1800 419 x +1800 643 1959 790 x +2119 939 2351 939 x +4824 fwd_x +end_ol + } def +/wAA { start_ol +4003 2088 m +790 2088 l +574 2088 574 2255 x +574 2415 790 2415 x +4003 2415 l +4219 2415 4219 2255 x +4219 2088 4003 2088 x +4824 fwd_x +end_ol + } def +/xAA { start_ol +3744 1220 m +3744 1561 3533 1771 x +3323 1982 3011 2050 x +2701 2120 2335 2205 x +1971 2290 1661 2383 x +1353 2477 1144 2732 x +936 2988 936 3393 x +936 3925 1355 4284 x +1775 4644 2407 4644 x +3109 4644 3600 4170 x +3600 4321 l +3600 4536 3760 4536 x +3927 4536 3927 4318 x +3927 3488 l +3927 3271 3760 3271 x +3607 3271 3600 3466 x +3575 3830 3240 4073 x +2905 4316 2431 4316 x +1924 4316 1594 4048 x +1263 3782 1263 3385 x +1263 3069 1476 2874 x +1688 2679 2002 2611 x +2317 2542 2679 2449 x +3043 2355 3350 2257 x +3657 2161 3864 1888 x +4071 1617 4071 1204 x +4071 615 3610 235 x +3148 -144 2432 -144 x +1563 -144 1047 434 x +1047 209 l +1047 0 907 0 x +720 0 720 216 x +720 1110 l +720 1326 916 1326 x +1040 1326 1047 1131 x +1064 734 1464 459 x +1866 183 2423 183 x +2990 183 3367 479 x +3744 775 3744 1220 x +4824 fwd_x +end_ol + } def +/yAA { start_ol +3999 0 m +3583 0 l +1119 4063 l +1119 327 l +1702 327 l +1911 327 1911 167 x +1911 0 1705 0 x +565 0 l +360 0 360 167 x +360 327 551 327 x +792 327 l +792 4208 l +408 4208 l +216 4208 216 4376 x +216 4536 417 4536 x +1208 4536 l +3672 472 l +3672 4208 l +3097 4208 l +2880 4208 2880 4376 x +2880 4536 3092 4536 x +4225 4536 l +4431 4536 4431 4376 x +4431 4208 4240 4208 x +3999 4208 l +3999 0 l +4824 fwd_x +end_ol + } def +/zAA { start_ol +1335 2048 m +1335 327 l +1918 327 l +2127 327 2127 167 x +2127 0 1922 0 x +636 0 l +432 0 432 167 x +432 327 624 327 x +1008 327 l +1008 4208 l +624 4208 l +432 4208 432 4376 x +432 4536 643 4536 x +2588 4536 l +3160 4536 3579 4164 x +3999 3794 3999 3291 x +3999 2518 2887 2136 x +3262 1874 3516 1539 x +3772 1203 4257 327 x +4504 327 l +4719 327 4719 167 x +4719 0 4504 0 x +4050 0 l +3523 995 3184 1415 x +2846 1836 2391 2048 x +1335 2048 l +1335 2376 m +2247 2376 l +2839 2376 3255 2647 x +3672 2918 3672 3300 x +3672 3658 3331 3933 x +2991 4208 2559 4208 x +1335 4208 l +1335 2376 l +4824 fwd_x +end_ol + } def +/ABA { start_ol +1479 1429 m +1479 0 l +720 0 l +504 0 504 167 x +504 327 720 327 x +1152 327 l +1152 4536 l +720 4536 l +504 4536 504 4703 x +504 4863 720 4863 x +1479 4863 l +1479 1819 l +2862 2984 l +2686 2984 l +2470 2984 2470 3152 x +2470 3312 2686 3312 x +3724 3312 l +3940 3312 3940 3152 x +3940 2984 3724 2984 x +3350 2984 l +2094 1945 l +3749 327 l +4108 327 l +4324 327 4324 167 x +4324 0 4108 0 x +3062 0 l +2846 0 2846 167 x +2846 327 3062 327 x +3286 327 l +1847 1739 l +1479 1429 l +4824 fwd_x +end_ol + } def +/BBA { start_ol +1335 2160 m +1335 327 l +2413 327 l +2631 327 2631 167 x +2631 0 2417 0 x +637 0 l +432 0 432 167 x +432 327 624 327 x +1008 327 l +1008 4208 l +624 4208 l +432 4208 432 4376 x +432 4536 642 4536 x +4143 4536 l +4143 3478 l +4143 3272 3975 3272 x +3816 3272 3816 3475 x +3816 4208 l +1335 4208 l +1335 2487 l +2448 2487 l +2448 2802 l +2448 2991 2607 2991 x +2775 2991 2775 2796 x +2775 1850 l +2775 1656 2607 1656 x +2448 1656 2448 1845 x +2448 2160 l +1335 2160 l +4824 fwd_x +end_ol + } def +/CBA { start_ol +4171 2664 m +623 2664 l +407 2664 407 2831 x +407 2991 623 2991 x +4171 2991 l +4387 2991 4387 2831 x +4387 2664 4171 2664 x +4171 1512 m +623 1512 l +407 1512 407 1679 x +407 1839 623 1839 x +4171 1839 l +4387 1839 4387 1679 x +4387 1512 4171 1512 x +4824 fwd_x +end_ol + } def +/DBA { start_ol +3664 4680 m +1330 4680 l +2721 2641 l +2769 2586 2769 2538 x +2769 2506 2737 2442 x +1282 -176 l +3744 -176 l +3782 675 l +3796 831 3903 831 x +3949 831 l +4071 831 4071 663 x +4071 -336 l +4071 -504 3900 -504 x +1179 -504 l +1008 -504 1008 -352 x +1008 -225 l +1008 -160 1039 -96 x +2486 2562 l +1055 4608 l +1008 4672 1008 4752 x +1008 4855 l +1008 5007 1182 5007 x +3897 5007 l +4071 5007 4071 4838 x +4071 3840 l +4071 3672 3926 3672 x +3881 3672 l +3754 3672 3736 3829 x +3664 4680 l +4824 fwd_x +end_ol + } def +/EBA { start_ol +504 2614 m +504 2767 547 2990 x +591 3213 726 3512 x +862 3811 1062 4053 x +1262 4296 1621 4469 x +1981 4644 2435 4644 x +3241 4644 3816 4089 x +3816 4321 l +3816 4536 3983 4536 x +4143 4536 4143 4318 x +4143 3415 l +4143 3198 3975 3198 x +3831 3198 3816 3393 x +3792 3765 3380 4041 x +2970 4316 2435 4316 x +1773 4316 1301 3801 x +831 3287 831 2566 x +831 1990 l +831 1261 1350 722 x +1868 183 2570 183 x +2985 183 3313 349 x +3640 516 3960 896 x +4032 975 4104 975 x +4264 975 4264 824 x +4264 752 4136 601 x +4008 451 3800 280 x +3593 110 3256 -16 x +2921 -144 2570 -144 x +1757 -144 1130 490 x +504 1126 504 1942 x +504 2614 l +4824 fwd_x +end_ol + } def +/FBA { start_ol +1217 3413 m +1686 3413 l +1686 1446 l +2872 2461 l +3422 2461 l +2337 1540 l +3594 14 l +3039 14 l +2021 1279 l +1686 994 l +1686 14 l +1217 14 l +1217 3413 l +4824 fwd_x +end_ol + } def +/GBA { start_ol +2507 3384 m +3201 3384 3708 2902 x +4215 2422 4215 1674 x +4215 946 3728 454 x +3242 -36 2507 -36 x +1630 -36 1119 680 x +1119 -1256 l +1859 -1256 l +2055 -1256 2055 -1411 x +2055 -1584 1860 -1584 x +417 -1584 l +216 -1584 216 -1411 x +216 -1256 408 -1256 x +792 -1256 l +792 1478 l +775 1621 l +775 2127 1046 2550 x +1318 2973 1725 3201 x +2076 3384 2507 3384 x +2507 3056 m +1885 3056 1501 2651 x +1119 2246 1119 1674 x +1119 1093 1522 691 x +1924 291 2507 291 x +3082 291 3485 696 x +3888 1101 3888 1674 x +3888 2262 3512 2659 x +3137 3056 2507 3056 x +4824 fwd_x +end_ol + } def +/HBA { start_ol +1217 6005 m +1686 6005 l +1686 4038 l +2872 5053 l +3422 5053 l +2337 4132 l +3594 2606 l +3039 2606 l +2021 3871 l +1686 3586 l +1686 2606 l +1217 2606 l +1217 6005 l +4824 fwd_x +end_ol + } def +/IBA { start_ol +970 4285 m +970 4368 1126 4521 x +1282 4674 1625 4822 x +1969 4971 2377 4971 x +2976 4971 3379 4614 x +3783 4258 3783 3737 x +3783 3272 3523 3000 x +3263 2728 2959 2648 x +3431 2454 3714 2112 x +3999 1771 3999 1361 x +3999 751 3507 321 x +3016 -108 2328 -108 x +1857 -108 1317 128 x +778 364 778 564 x +778 621 825 669 x +874 717 930 717 x +986 717 1154 592 x +1321 468 1633 343 x +1945 219 2336 219 x +2880 219 3276 556 x +3672 895 3672 1361 x +3672 1836 3245 2178 x +2820 2520 2233 2520 x +2016 2520 2016 2687 x +2016 2847 2227 2847 x +3456 2847 3456 3729 x +3456 4123 3144 4383 x +2832 4644 2369 4644 x +2034 4644 1797 4566 x +1562 4488 1470 4392 x +1378 4295 1290 4217 x +1202 4140 1130 4140 x +1066 4140 1018 4181 x +970 4224 970 4285 x +4824 fwd_x +end_ol + } def +/JBA { start_ol +1119 4863 m +1119 2601 l +1716 3420 2592 3420 x +3333 3420 3846 2911 x +4359 2404 4359 1666 x +4359 913 3841 384 x +3325 -144 2592 -144 x +1692 -144 1119 699 x +1119 0 l +360 0 l +144 0 144 154 x +144 327 360 327 x +792 327 l +792 4536 l +360 4536 l +144 4536 144 4703 x +144 4863 360 4863 x +1119 4863 l +2576 3092 m +1969 3092 1544 2671 x +1119 2252 1119 1650 x +1119 1048 1544 615 x +1969 183 2576 183 x +3172 183 3602 608 x +4032 1033 4032 1626 x +4032 2244 3610 2668 x +3189 3092 2576 3092 x +4824 fwd_x +end_ol + } def +/KBA { start_ol +2629 1739 m +4099 327 l +4171 327 l +4387 327 4387 167 x +4387 0 4171 0 x +3117 0 l +2901 0 2901 167 x +2901 327 3117 327 x +3636 327 l +2397 1509 l +1143 327 l +1686 327 l +1902 327 1902 167 x +1902 0 1686 0 x +623 0 l +407 0 407 167 x +407 327 623 327 x +695 327 l +2165 1739 l +862 2984 l +807 2984 l +591 2984 591 3152 x +591 3312 807 3312 x +1694 3312 l +1910 3312 1910 3152 x +1910 2984 1694 2984 x +1326 2984 l +2397 1953 l +3492 2984 l +3108 2984 l +2893 2984 2893 3152 x +2893 3312 3108 3312 x +3988 3312 l +4204 3312 4204 3152 x +4204 2984 3988 2984 x +3931 2984 l +2629 1739 l +4824 fwd_x +end_ol + } def +/LBA { start_ol +1839 4208 m +1839 327 l +3960 327 l +3960 1559 l +3960 1767 4127 1767 x +4287 1767 4287 1558 x +4287 0 l +785 0 l +576 0 576 167 x +576 327 781 327 x +1512 327 l +1512 4208 l +781 4208 l +576 4208 576 4376 x +576 4536 783 4536 x +2568 4536 l +2775 4536 2775 4376 x +2775 4208 2569 4208 x +1839 4208 l +4824 fwd_x +end_ol + } def +/MBA { start_ol +1335 1832 m +1335 327 l +2413 327 l +2631 327 2631 167 x +2631 0 2417 0 x +637 0 l +432 0 432 167 x +432 327 624 327 x +1008 327 l +1008 4208 l +624 4208 l +432 4208 432 4376 x +432 4536 643 4536 x +2521 4536 l +3146 4536 3573 4151 x +3999 3766 3999 3192 x +3999 2619 3528 2225 x +3057 1832 2380 1832 x +1335 1832 l +1335 2160 m +2404 2160 l +2922 2160 3297 2462 x +3672 2766 3672 3192 x +3672 3610 3332 3909 x +2993 4208 2523 4208 x +1335 4208 l +1335 2160 l +4824 fwd_x +end_ol + } def +/NBA { start_ol +1654 1165 m +2718 1165 l +1559 -951 l +1455 -1152 1311 -1152 x +1216 -1152 1147 -1083 x +1080 -1015 1080 -920 x +1080 -896 1095 -832 x +1654 1165 l +4824 fwd_x +end_ol + } def +/PBA { start_ol +3547 -507 m +2715 -507 l +1264 2407 l +2715 5326 l +3547 5326 l +2088 2407 l +3547 -507 l +4824 fwd_x +end_ol + } def +/QBA { start_ol +3855 2829 m +3855 2026 l +3855 1080 3447 486 x +3039 -108 2395 -108 x +1751 -108 1343 486 x +936 1080 936 2026 x +936 2829 l +936 3783 1343 4377 x +1751 4971 2395 4971 x +3039 4971 3447 4377 x +3855 3783 3855 2829 x +2395 219 m +2922 219 3225 779 x +3528 1339 3528 2109 x +3528 2264 l +1263 2264 l +1263 2109 l +1263 1307 1577 762 x +1891 219 2395 219 x +2395 4644 m +1868 4644 1566 4097 x +1263 3550 1263 2800 x +1263 2592 l +3528 2592 l +3528 2800 l +3528 3582 3214 4113 x +2900 4644 2395 4644 x +4824 fwd_x +end_ol + } def +/RBA { start_ol +4359 1040 m +4359 849 4309 686 x +4261 524 4138 356 x +4016 190 3755 94 x +3494 0 3126 0 x +2775 0 l +2775 -1584 l +2448 -1584 l +2448 0 l +2084 0 l +1575 0 1255 277 x +936 556 936 1027 x +936 2984 l +541 2984 l +288 2984 288 3155 x +288 3312 573 3312 x +1303 3312 l +1303 1047 l +1303 723 1510 525 x +1717 327 2041 327 x +2448 327 l +2448 3312 l +3232 3312 l +3551 3312 3786 3208 x +4023 3105 4138 2938 x +4255 2772 4307 2601 x +4359 2430 4359 2255 x +4359 1040 l +3231 335 m +3660 335 3846 561 x +4032 787 4032 1049 x +4032 2262 l +4032 2968 3188 2968 x +2775 2968 l +2775 335 l +3231 335 l +4824 fwd_x +end_ol + } def +/SBA { start_ol +3008 5592 m +3008 -956 l +1803 -956 l +1803 5592 l +3008 5592 l +4824 fwd_x +end_ol + } def +/TBA { start_ol +2823 1440 m +3186 1440 3537 1845 x +3888 2250 3888 2810 x +3888 4536 l +4487 4536 l +4703 4536 4703 4365 x +4703 4216 4487 4216 x +4215 4216 l +4215 2814 l +4215 2440 4098 2130 x +3982 1821 3814 1638 x +3648 1454 3445 1332 x +3243 1210 3088 1165 x +2932 1120 2823 1120 x +2631 1104 l +2631 327 l +2872 327 l +3063 327 3063 167 x +3063 0 2860 0 x +2081 0 l +1872 0 1872 167 x +1872 327 2070 327 x +2304 327 l +2304 1104 l +2124 1112 l +1969 1112 1749 1193 x +1528 1275 1267 1450 x +1006 1625 826 1980 x +648 2334 648 2799 x +648 4208 l +371 4208 l +290 4208 217 4251 x +144 4294 144 4365 x +144 4536 372 4536 x +975 4536 l +975 2793 l +975 2226 1345 1832 x +1716 1440 2116 1440 x +2304 1432 l +2304 4208 l +2142 4208 l +2071 4208 2007 4254 x +1944 4302 1944 4365 x +1944 4536 2155 4536 x +2787 4536 l +2901 4520 2946 4493 x +2991 4466 2991 4365 x +2991 4208 2801 4208 x +2631 4208 l +2631 1432 l +2823 1440 l +4824 fwd_x +end_ol + } def +/UBA { start_ol +1264 -507 m +2720 2407 l +1267 5326 l +2095 5326 l +3547 2407 l +2095 -507 l +1264 -507 l +4824 fwd_x +end_ol + } def +/VBA { start_ol +2376 1941 m +2376 2533 2613 3240 x +2851 3947 3116 4387 x +3381 4827 3498 4827 x +3561 4827 3607 4779 x +3655 4731 3655 4667 x +3655 4579 3531 4343 x +3408 4107 3259 3823 x +3109 3540 2985 3020 x +2863 2502 2863 1918 x +2863 695 3631 -743 x +3655 -798 3655 -831 x +3655 -895 3604 -942 x +3553 -991 3490 -991 x +3366 -991 3105 -555 x +2844 -120 2610 598 x +2376 1318 2376 1941 x +4824 fwd_x +end_ol + } def +/WBA { start_ol +1224 -831 m +1224 -743 1346 -507 x +1470 -272 1620 11 x +1769 295 1892 814 x +2016 1334 2016 1918 x +2016 3148 1247 4579 x +1224 4635 1224 4667 x +1224 4731 1274 4779 x +1325 4827 1388 4827 x +1513 4827 1774 4390 x +2035 3955 2269 3236 x +2503 2517 2503 1894 x +2503 1302 2264 595 x +2027 -111 1761 -551 x +1497 -991 1380 -991 x +1317 -991 1270 -942 x +1224 -895 1224 -831 x +4824 fwd_x +end_ol + } def +/XBA { start_ol +1447 -288 m +1519 -666 1779 -888 x +2039 -1112 2414 -1112 x +2686 -1112 2921 -1032 x +3157 -954 3285 -867 x +3349 -824 3405 -824 x +3477 -824 3524 -873 x +3573 -921 3573 -979 x +3573 -1024 3549 -1068 x +3444 -1217 3081 -1328 x +2718 -1440 2406 -1440 x +1855 -1440 1467 -1059 x +1080 -679 1080 -131 x +1080 335 1443 654 x +1806 975 2334 975 x +2885 975 3241 648 x +3597 320 3597 -220 x +3597 -288 l +1447 -288 l +1447 39 m +3222 39 l +3142 317 2905 482 x +2670 648 2335 648 x +2007 648 1770 486 x +1535 325 1447 39 x +4824 fwd_x +end_ol + } def +/YBA { start_ol +2513 901 m +2513 631 2622 492 x +2731 354 2949 354 x +3480 354 l +3480 14 l +2911 14 l +2505 14 2282 246 x +2061 479 2061 901 x +2061 3125 l +1334 3125 l +1334 3441 l +2513 3441 l +2513 901 l +4824 fwd_x +end_ol + } def +/ZBA { start_ol +2247 562 m +2279 499 l +2154 31 1873 -624 x +1561 -624 l +1686 -31 1779 562 x +2247 562 l +4032 fwd_x +end_ol + } def +/aBA { start_ol +2540 2211 m +2622 2371 2750 2445 x +2880 2520 3063 2520 x +3395 2520 3531 2291 x +3668 2063 3668 1431 x +3668 14 l +3254 14 l +3254 1415 l +3254 1935 3188 2059 x +3121 2184 2949 2184 x +2755 2184 2683 2049 x +2611 1914 2611 1415 x +2611 14 l +2197 14 l +2197 1415 l +2197 1938 2126 2061 x +2056 2184 1873 2184 x +1693 2184 1624 2049 x +1557 1914 1557 1415 x +1557 14 l +1143 14 l +1143 2461 l +1557 2461 l +1557 2251 l +1634 2383 1757 2451 x +1881 2520 2032 2520 x +2220 2520 2345 2443 x +2470 2368 2540 2211 x +4824 fwd_x +end_ol + } def +/bBA { start_ol +3999 4208 m +3999 1481 l +3999 794 3535 325 x +3073 -144 2396 -144 x +1711 -144 1251 320 x +792 786 792 1481 x +792 4208 l +551 4208 l +360 4208 360 4376 x +360 4536 565 4536 x +1705 4536 l +1911 4536 1911 4376 x +1911 4208 1699 4208 x +1119 4208 l +1119 1479 l +1119 928 1486 555 x +1854 183 2395 183 x +2928 183 3299 560 x +3672 937 3672 1479 x +3672 4208 l +3091 4208 l +2880 4208 2880 4376 x +2880 4536 3085 4536 x +4225 4536 l +4431 4536 4431 4376 x +4431 4208 4240 4208 x +3999 4208 l +4824 fwd_x +end_ol + } def +/cBA { start_ol +3816 5059 m +1263 -504 l +1193 -646 1092 -646 x +1029 -646 982 -598 x +936 -551 936 -495 x +936 -455 975 -367 x +3528 5195 l +3589 5338 3699 5338 x +3762 5338 3808 5289 x +3855 5242 3855 5186 x +3855 5139 3816 5059 x +4824 fwd_x +end_ol + } def +end end +%%EndPrologue +%%EndPrologue +%%Page: 1 1 +paps_bop +(+ 36000 807000AAABAACAA+ 64800 807000EAAFAAGAA+ 93600 807000HAAIAA+ 115200 807000JAAKAALAAMAAHAALAANAAMAA+ 180000 807000HAAOAAJAAPAA)paps_exec +(* 290300QAARAA)paps_exec +(* 515800SAAFAATAACAA+ 551800 807000JAA)paps_exec +36 797.000000 moveto 559 797.000000 lineto 0 setlinewidth stroke +(+ 36000 782936UAAVAAWAAXAAYAAZAA+ 69768 782936XAAbAA+ 84240 782936cAAVAAWAA+ 103536 782936dAAZAAeAAYAAXAAfAAWAAgAA+ 146952 782936hAAcAAXAAiAA)paps_exec +(+ 36000 774872jAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAAjAA)paps_exec +()paps_exec +(+ 55296 758744kAAWAAYAAlAAmAAWAAeAA+ 93888 758744bAAYAAXAAiAA+ 118008 758744bAAlAAYAAnAAcAA+ 146952 758744oAAYAAlAAgAApAAlAAoAAqAAWAAnAA+ 200016 758744cAAVAAWAA+ 219312 758744rAAsAAmAAWAA+ 243432 758744WAAtAAuAAsAAcAAlAAXAAgAA+ 286848 758744XAAbAA+ 301320 758744sAAgAA+ 315792 758744WAAqAAWAApAAcAAYAAXAAgAA+ 359208 758744lAAgAA+ 373680 758744cAAVAAWAA)paps_exec +(+ 55296 750680VAAZAAeAAYAAXAAfAAWAAgAA+ 98712 750680sAAcAAXAAiAAvAA)paps_exec +()paps_exec +(+ 74592 734552wAA+ 84240 734552xAAcAAsAAYAAcAA+ 113184 734552rAAlAAcAAVAA+ 137304 734552kAAlAAYAAsAApAA+ 166248 734552yAAXAAcAAsAAcAAlAAXAAgAA)paps_exec +(+ 74592 726488wAA+ 84240 726488zAAWAAoAAqAAsAApAAWAA+ 122832 726488rAAlAAcAAVAA+ 146952 726488ABAgAAXAArAAgAA+ 175896 726488fAAWAAgAAWAAYAAsAAqAA+ 214488 726488bAAuAAgAApAAcAAlAAXAAgAAnAA)paps_exec +(+ 74592 718424wAA+ 84240 718424cAAYAAsAAgAAnAAbAAXAAYAAiAA+ 132480 718424cAAXAA+ 146952 718424WAAlAAfAAWAAgAAmAAsAAqAAuAAWAA+ 200016 718424WAAtAAuAAsAAcAAlAAXAAgAA+ 243432 718424lAAgAA+ 257904 718424oAAXAAnAAlAAcAAlAAXAAgAA+ 301320 718424nAAoAAsAApAAWAA)paps_exec +(+ 74592 710360wAA+ 84240 710360YAAWAAoAAqAAsAApAAWAA+ 122832 710360oAAlAAWAApAAWAAnAA+ 156600 710360rAAlAAcAAVAA+ 180720 710360bAAuAAgAApAAcAAlAAXAAgAA+ 224136 710360BBA+ 233784 710360sAAgAAeAA+ 253080 710360bAAlAAgAAeAA+ 277200 710360eAAWAAYAAlAAmAAsAAcAAlAAmAAWAAnAA)paps_exec +(+ 93888 700928BBA+ 103536 700928CBA+ 113184 700928DBA+ 122832 700928EBAFBAGBAHBA)paps_exec +()paps_exec +(+ 74592 684800oAAlAApAA+ 93888 684800IBA+ 103536 684800bAAlAAYAAnAAcAA+ 132480 684800cAAsAAABAWAA+ 156600 684800VAAsAAeAA+ 175896 684800bAAsAApAAcAAXAAYAAnAA+ 214488 684800cAAVAAsAAcAA+ 238608 684800gAAWAAWAAeAAWAAeAA+ 272376 684800cAAXAA+ 286848 684800JBAWAA+ 301320 684800bAAlAAKBAWAAeAA)paps_exec +()paps_exec +(+ 74592 668672wAA+ 84240 668672LBAWAAeAA+ 103536 668672cAAXAA+ 118008 668672cAAVAAWAA+ 137304 668672LBAsAAfAAuAAWAAYAAYAAWAA+ 180720 668672MBAXAAqAAZAAgAAXAAiAAlAAsAAqAAnAA)paps_exec +(+ 93888 660608UAAVAAWAAnAAWAA+ 122832 660608sAAYAAWAA+ 142128 660608lAAgAAbAAlAAgAAlAAcAAWAANBA+ 190368 660608cAAVAAXAAuAAfAAVAANBA+ 228960 660608nAAXAA)paps_exec +(+ 74592 652544wAA+ 84240 652544BBAXAAYAApAAWAA+ 113184 652544LBAsAAfAAuAAWAAYAAYAAWAA+ 156600 652544MBAXAAqAAZAAgAAXAAiAAlAAsAAqAA+ 209664 652544nAAXAAqAAuAAcAAlAAXAAgAAnAA+ 257904 652544cAAXAA+ 272376 652544cAAYAAuAAgAApAAsAAcAAWAA)paps_exec +()paps_exec +(+ 36000 636416kAAWAAYAAlAAmAAsAAcAAlAAXAAgAA)paps_exec +(+ 36000 628352jAAjAAjAAjAAjAAjAAjAAjAAjAAjAA)paps_exec +(+ 55296 620288UAAVAAWAA+ 74592 620288eAAlAAbAAbAAWAAYAAWAAgAAcAAlAAsAAqAA+ 137304 620288WAAtAAuAAsAAcAAlAAXAAgAA+ 180720 620288lAAnAA+ 195192 620288nAAWAAoAAsAAYAAsAAJBAqAAWAAvAA)paps_exec +()paps_exec +(+ 55296 601712PBAYAANBAQBANBARBASBATBAUBA+ 103536 601712CBA+ 113184 601712zAAVBAYAAWBAXBANBAYBA+ 151776 601712ZAAYBAZBAaBAVBAQBANBARBAWBA)paps_exec +()paps_exec +(+ 55296 583136zAAXBAZBAYBAVBAYAAWBA+ 93096 583136CBA+ 102744 583136bBAXBAZBAYBAVBAYAAWBA+ 140544 583136cBAYAA)paps_exec +()paps_exec +()paps_exec +()paps_exec +()paps_exec +paps_eop +showpage +%%Pages: 1 +%%Trailer +%%EOF