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% 
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% 
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% 
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% 
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% DOT 1 0 3 0
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% 
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% DOT 1 0 3 0
% 2 820 1000 820 1000
% 
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% DOT 1 0 3 0
% 2 1300 1000 1300 1000
% 
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\special{sh 1}%
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% DOT 1 0 3 0
% 2 1192 796 1192 796
% 
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\special{sh 1}%
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% DOT 1 0 3 0
% 2 844 892 844 892
% 
\special{pn 13}%
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\special{sh 1}%
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% DOT 1 0 3 0
% 2 1276 880 1276 880
% 
\special{pn 13}%
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% BOX 2 5 2 0
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% 
\special{pn 8}%
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% LINE 2 1 3 0
% 4 2994 1802 2990 1802 2990 1802 3800 1802
% 
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% 
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% 
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% 
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% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
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% 
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% CIRCLE 2 0 0 0
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% 
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% 
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% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
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% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% 4 22960 1600 23740 1600 23740 1600 23740 1600
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% 4 25380 1580 26160 1580 26160 1580 26160 1580
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
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% 4 18200 1600 18980 1600 18980 1600 18980 1600
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% 4 20580 1600 21360 1600 21360 1600 21360 1600
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% 4 22960 1600 23740 1600 23740 1600 23740 1600
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
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\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
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% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
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\special{pn 8}%
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
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% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
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% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
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% 4 25380 1580 26160 1580 26160 1580 26160 1580
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% 4 27760 1580 28540 1580 28540 1580 28540 1580
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% 4 18200 1600 18980 1600 18980 1600 18980 1600
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% 4 20580 1600 21360 1600 21360 1600 21360 1600
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% 4 22960 1600 23740 1600 23740 1600 23740 1600
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% 4 18200 1600 18980 1600 18980 1600 18980 1600
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% 4 20580 1600 21360 1600 21360 1600 21360 1600
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% 4 25380 1580 26160 1580 26160 1580 26160 1580
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% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% SPLINE 2 0 3 0
% 12 3160 1800 3126 1774 3196 1704 3205 1588 3313 1584 3382 1510 3472 1588 3568 1582 3574 1690 3649 1768 3622 1804 3622 1804
% 
\special{pn 8}%
\special{pa 3160 1400}%
\special{pa 3131 1380}%
\special{pa 3129 1362}%
\special{pa 3155 1342}%
\special{pa 3186 1317}%
\special{pa 3203 1284}%
\special{pa 3204 1246}%
\special{pa 3200 1211}%
\special{pa 3204 1189}%
\special{pa 3226 1184}%
\special{pa 3260 1189}%
\special{pa 3298 1189}%
\special{pa 3329 1172}%
\special{pa 3353 1143}%
\special{pa 3371 1117}%
\special{pa 3389 1111}%
\special{pa 3409 1130}%
\special{pa 3432 1159}%
\special{pa 3461 1183}%
\special{pa 3497 1190}%
\special{pa 3534 1183}%
\special{pa 3562 1180}%
\special{pa 3573 1194}%
\special{pa 3570 1226}%
\special{pa 3568 1264}%
\special{pa 3579 1299}%
\special{pa 3607 1325}%
\special{pa 3636 1345}%
\special{pa 3649 1366}%
\special{pa 3635 1391}%
\special{pa 3622 1404}%
\special{sp}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 18200 1600 18980 1600 18980 1600 18980 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 18200 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 20580 1600 21360 1600 21360 1600 21360 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 20580 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 22960 1600 23740 1600 23740 1600 23740 1600
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 22960 1200 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 25380 1580 26160 1580 26160 1580 26160 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 25380 1180 780 780  0.0000000 6.2831853}%
% CIRCLE 2 0 0 0
% 4 27760 1580 28540 1580 28540 1580 28540 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{ar 27760 1180 780 780  0.0000000 6.2831853}%
% SPLINE 2 0 3 0
% 18 4604 1800 4564 1700 4454 1740 4504 1640 4404 1600 4504 1560 4454 1460 4564 1500 4604 1400 4644 1500 4754 1460 4704 1560 4804 1600 4704 1640 4754 1740 4644 1700 4604 1800 4604 1800
% 
\special{pn 8}%
\special{pa 4604 1400}%
\special{pa 4600 1358}%
\special{pa 4592 1323}%
\special{pa 4574 1303}%
\special{pa 4542 1303}%
\special{pa 4503 1318}%
\special{pa 4469 1335}%
\special{pa 4454 1340}%
\special{pa 4466 1323}%
\special{pa 4489 1291}%
\special{pa 4506 1256}%
\special{pa 4494 1228}%
\special{pa 4457 1212}%
\special{pa 4419 1204}%
\special{pa 4404 1200}%
\special{pa 4427 1195}%
\special{pa 4467 1185}%
\special{pa 4500 1167}%
\special{pa 4504 1135}%
\special{pa 4484 1099}%
\special{pa 4461 1070}%
\special{pa 4455 1060}%
\special{pa 4476 1073}%
\special{pa 4512 1094}%
\special{pa 4551 1103}%
\special{pa 4579 1086}%
\special{pa 4595 1047}%
\special{pa 4601 1011}%
\special{pa 4605 1001}%
\special{pa 4609 1026}%
\special{pa 4619 1066}%
\special{pa 4640 1098}%
\special{pa 4675 1101}%
\special{pa 4714 1084}%
\special{pa 4745 1065}%
\special{pa 4753 1061}%
\special{pa 4737 1082}%
\special{pa 4713 1116}%
\special{pa 4702 1151}%
\special{pa 4721 1177}%
\special{pa 4760 1191}%
\special{pa 4795 1197}%
\special{pa 4801 1201}%
\special{pa 4772 1207}%
\special{pa 4732 1218}%
\special{pa 4704 1240}%
\special{pa 4708 1272}%
\special{pa 4730 1307}%
\special{pa 4751 1334}%
\special{pa 4750 1340}%
\special{pa 4725 1328}%
\special{pa 4686 1310}%
\special{pa 4649 1300}%
\special{pa 4624 1310}%
\special{pa 4611 1338}%
\special{pa 4606 1377}%
\special{pa 4604 1400}%
\special{sp}%
% DOT 1 0 3 0
% 2 2068 796 2068 796
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2068 396 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2068 396 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 2200 760 2200 760
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2200 360 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2200 360 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 1960 1000 1960 1000
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1960 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1960 600 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 2440 1000 2440 1000
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2440 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2440 600 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 2332 796 2332 796
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2332 396 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2332 396 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 1984 892 1984 892
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1984 492 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1984 492 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 2 2416 880 2416 880
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2416 480 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2416 480 10 10 0  6.28318530717959E+0000}%
% LINE 2 1 3 0
% 4 4214 1800 4210 1800 4210 1800 5020 1800
% 
\special{pn 8}%
\special{pa 4214 1400}%
\special{pa 4210 1400}%
\special{da 0.070}%
\special{pa 4210 1400}%
\special{pa 5020 1400}%
\special{da 0.070}%
% POLYGON 2 0 0 0
% 4 2200 730 2200 790 2148 760 2200 730
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2200 330}%
\special{pa 2200 390}%
\special{pa 2148 360}%
\special{pa 2200 330}%
\special{fp}%
% LINE 2 1 3 0
% 4 634 1005 630 1005 630 1005 1440 1005
% 
\special{pn 8}%
\special{pa 634 605}%
\special{pa 630 605}%
\special{da 0.070}%
\special{pa 630 605}%
\special{pa 1440 605}%
\special{da 0.070}%
% POLYGON 2 0 0 0
% 4 1060 980 1060 1040 1008 1010 1060 980
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 1060 580}%
\special{pa 1060 640}%
\special{pa 1008 610}%
\special{pa 1060 580}%
\special{fp}%
% LINE 2 1 3 0
% 4 1794 1005 1790 1005 1790 1005 2600 1005
% 
\special{pn 8}%
\special{pa 1794 605}%
\special{pa 1790 605}%
\special{da 0.070}%
\special{pa 1790 605}%
\special{pa 2600 605}%
\special{da 0.070}%
% POLYGON 2 0 0 0
% 4 2220 980 2220 1040 2168 1010 2220 980
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2220 580}%
\special{pa 2220 640}%
\special{pa 2168 610}%
\special{pa 2220 580}%
\special{fp}%
% LINE 2 1 3 0
% 4 604 1795 600 1795 600 1795 1410 1795
% 
\special{pn 8}%
\special{pa 604 1395}%
\special{pa 600 1395}%
\special{da 0.070}%
\special{pa 600 1395}%
\special{pa 1410 1395}%
\special{da 0.070}%
% DOT 1 0 3 0
% 3 930 1400 1090 1400 1090 1400
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 930 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1090 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1090 1000 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 970 1400 1050 1400
% 
\special{pn 8}%
\special{pa 970 1000}%
\special{pa 1050 1000}%
\special{fp}%
% DOT 1 0 3 0
% 3 1210 1520 1210 1680 1210 1680
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1210 1120 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1210 1280 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1210 1280 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 1210 1560 1210 1640
% 
\special{pn 8}%
\special{pa 1210 1160}%
\special{pa 1210 1240}%
\special{fp}%
% DOT 1 0 3 0
% 3 810 1520 810 1680 810 1680
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 810 1120 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 810 1280 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 810 1280 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 810 1560 810 1640
% 
\special{pn 8}%
\special{pa 810 1160}%
\special{pa 810 1240}%
\special{fp}%
% LINE 2 0 3 0
% 2 1130 1420 1190 1480
% 
\special{pn 8}%
\special{pa 1130 1020}%
\special{pa 1190 1080}%
\special{fp}%
% LINE 2 0 3 0
% 2 830 1710 890 1770
% 
\special{pn 8}%
\special{pa 830 1310}%
\special{pa 890 1370}%
\special{fp}%
% LINE 2 0 3 0
% 2 890 1420 830 1480
% 
\special{pn 8}%
\special{pa 890 1020}%
\special{pa 830 1080}%
\special{fp}%
% LINE 2 0 3 0
% 2 1170 1720 1110 1780
% 
\special{pn 8}%
\special{pa 1170 1320}%
\special{pa 1110 1380}%
\special{fp}%
% DOT 1 0 3 0
% 3 930 1800 1090 1800 1090 1800
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 930 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1090 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1090 1400 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 970 1800 1050 1800
% 
\special{pn 8}%
\special{pa 970 1400}%
\special{pa 1050 1400}%
\special{fp}%
% LINE 2 1 3 0
% 4 1764 1795 1760 1795 1760 1795 2570 1795
% 
\special{pn 8}%
\special{pa 1764 1395}%
\special{pa 1760 1395}%
\special{da 0.070}%
\special{pa 1760 1395}%
\special{pa 2570 1395}%
\special{da 0.070}%
% DOT 1 0 3 0
% 3 2090 1400 2250 1400 2250 1400
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2090 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2250 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2250 1000 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 2130 1400 2210 1400
% 
\special{pn 8}%
\special{pa 2130 1000}%
\special{pa 2210 1000}%
\special{fp}%
% DOT 1 0 3 0
% 3 2370 1520 2370 1680 2370 1680
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2370 1120 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2370 1280 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2370 1280 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 2370 1560 2370 1640
% 
\special{pn 8}%
\special{pa 2370 1160}%
\special{pa 2370 1240}%
\special{fp}%
% DOT 1 0 3 0
% 3 1970 1520 1970 1680 1970 1680
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1970 1120 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1970 1280 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1970 1280 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 1970 1560 1970 1640
% 
\special{pn 8}%
\special{pa 1970 1160}%
\special{pa 1970 1240}%
\special{fp}%
% LINE 2 0 3 0
% 2 2290 1420 2350 1480
% 
\special{pn 8}%
\special{pa 2290 1020}%
\special{pa 2350 1080}%
\special{fp}%
% LINE 2 0 3 0
% 2 1990 1710 2050 1770
% 
\special{pn 8}%
\special{pa 1990 1310}%
\special{pa 2050 1370}%
\special{fp}%
% LINE 2 0 3 0
% 2 2050 1420 1990 1480
% 
\special{pn 8}%
\special{pa 2050 1020}%
\special{pa 1990 1080}%
\special{fp}%
% LINE 2 0 3 0
% 2 2330 1720 2270 1780
% 
\special{pn 8}%
\special{pa 2330 1320}%
\special{pa 2270 1380}%
\special{fp}%
% DOT 1 0 3 0
% 3 2090 1800 2250 1800 2250 1800
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2090 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2250 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2250 1400 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 2130 1800 2210 1800
% 
\special{pn 8}%
\special{pa 2130 1400}%
\special{pa 2210 1400}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 2340 1580 2400 1580 2370 1632 2340 1580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2340 1180}%
\special{pa 2400 1180}%
\special{pa 2370 1232}%
\special{pa 2340 1180}%
\special{fp}%
% BOX 2 5 2 0
% 2 4240 855 4240 815
% 
\special{pn 8}%
\special{sh 0}%
\special{pa 4240 455}%
\special{pa 4240 455}%
\special{pa 4240 415}%
\special{pa 4240 415}%
\special{pa 4240 455}%
\special{ip}%
% CIRCLE 2 0 3 0
% 4 4630 810 4430 810 4430 810 5000 810
% 
\special{pn 8}%
\special{ar 4630 410 200 200  6.2831853 6.2831853}%
\special{ar 4630 410 200 200  0.0000000 3.1415927}%
% CIRCLE 1 0 3 0
% 4 4630 810 4830 810 4830 810 4260 810
% 
\special{pn 13}%
\special{ar 4630 410 200 200  3.1415927 6.2831853}%
% CIRCLE 2 0 3 0
% 4 3390 830 3390 630 3390 630 3390 630
% 
\special{pn 8}%
\special{ar 3390 430 200 200  0.0000000 6.2831853}%
% CIRCLE 2 0 3 0
% 4 3390 830 3620 830 3780 830 3000 830
% 
\special{pn 8}%
\special{ar 3390 430 230 230  3.1415927 6.2831853}%
% LINE 2 1 3 0
% 2 3190 830 2990 830
% 
\special{pn 8}%
\special{pa 3190 430}%
\special{pa 2990 430}%
\special{da 0.070}%
% LINE 2 1 3 0
% 2 3800 830 3600 830
% 
\special{pn 8}%
\special{pa 3800 430}%
\special{pa 3600 430}%
\special{da 0.070}%
% LINE 2 1 3 0
% 2 4420 820 4220 820
% 
\special{pn 8}%
\special{pa 4420 420}%
\special{pa 4220 420}%
\special{da 0.070}%
% LINE 2 1 3 0
% 2 5020 810 4820 810
% 
\special{pn 8}%
\special{pa 5020 410}%
\special{pa 4820 410}%
\special{da 0.070}%
% POLYGON 2 0 0 0
% 4 3400 590 3400 650 3348 620 3400 590
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3400 190}%
\special{pa 3400 250}%
\special{pa 3348 220}%
\special{pa 3400 190}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 4640 580 4640 640 4588 610 4640 580
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 4640 180}%
\special{pa 4640 240}%
\special{pa 4588 210}%
\special{pa 4640 180}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 3370 1060 3370 1000 3422 1030 3370 1060
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3370 660}%
\special{pa 3370 600}%
\special{pa 3422 630}%
\special{pa 3370 660}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 4610 1040 4610 980 4662 1010 4610 1040
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 4610 640}%
\special{pa 4610 580}%
\special{pa 4662 610}%
\special{pa 4610 640}%
\special{fp}%
% STR 2 0 3 0
% 3 1050 540 1050 640 5 0
% $\alpha$
\put(10.5000,-2.4000){\makebox(0,0){$\alpha$}}%
% STR 2 0 3 0
% 3 2200 530 2200 630 5 0
% $\beta$
\put(22.0000,-2.3000){\makebox(0,0){$\beta$}}%
% STR 2 0 3 0
% 3 1340 1490 1340 1590 5 0
% $\sigma$
\put(13.4000,-11.9000){\makebox(0,0){$\sigma$}}%
% STR 2 0 3 0
% 3 2520 1490 2520 1590 5 0
% $\tau$
\put(25.2000,-11.9000){\makebox(0,0){$\tau$}}%
% STR 2 0 3 0
% 3 3390 1300 3390 1400 5 0
% $A_\mu$
\put(33.9000,-10.0000){\makebox(0,0){$A_\mu$}}%
% STR 2 0 3 0
% 3 3380 430 3380 530 5 0
% $c$
\put(33.8000,-1.3000){\makebox(0,0){$c$}}%
% STR 2 0 3 0
% 3 4620 430 4620 530 5 0
% $e$
\put(46.2000,-1.3000){\makebox(0,0){$e$}}%
% POLYGON 2 0 0 0
% 4 3410 1770 3410 1830 3358 1800 3410 1770
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3410 1370}%
\special{pa 3410 1430}%
\special{pa 3358 1400}%
\special{pa 3410 1370}%
\special{fp}%
\end{picture}%
%WinTpicVersion2.15
\unitlength 0.1in
\begin{picture}(47.80,26.80)(12.50,-28.40)
% DOT 1 2 3 0
% 6 2995 990 2995 1190 2995 1390 2995 1090 2995 1290 2995 1290
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2995 590 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2995 790 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2995 990 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2995 690 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2995 890 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2995 890 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 3695 990 3695 1190 3695 1390 3695 1090 3695 1290 3695 1290
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 3695 590 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3695 790 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3695 990 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3695 690 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3695 890 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3695 890 10 10 0  6.28318530717959E+0000}%
% LINE 0 0 3 0
% 2 3495 790 3895 790
% 
\special{pn 20}%
\special{pa 3495 390}%
\special{pa 3895 390}%
\special{fp}%
% LINE 2 0 3 0
% 2 2795 770 3195 770
% 
\special{pn 8}%
\special{pa 2795 370}%
\special{pa 3195 370}%
\special{fp}%
% LINE 2 0 3 0
% 2 2795 810 3195 810
% 
\special{pn 8}%
\special{pa 2795 410}%
\special{pa 3195 410}%
\special{fp}%
% CIRCLE 2 0 3 0
% 4 2995 790 2995 590 3195 790 2795 790
% 
\special{pn 8}%
\special{ar 2995 390 200 200  3.1415927 6.2831853}%
% CIRCLE 2 0 3 0
% 4 3695 790 3695 590 3895 790 3495 790
% 
\special{pn 8}%
\special{ar 3695 390 200 200  3.1415927 6.2831853}%
% POLYGON 2 0 0 0
% 4 2995 620 2995 560 3047 590 2995 620
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2995 220}%
\special{pa 2995 160}%
\special{pa 3047 190}%
\special{pa 2995 220}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 3695 620 3695 560 3747 590 3695 620
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3695 220}%
\special{pa 3695 160}%
\special{pa 3747 190}%
\special{pa 3695 220}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 2995 760 2995 820 2943 790 2995 760
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2995 360}%
\special{pa 2995 420}%
\special{pa 2943 390}%
\special{pa 2995 360}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 3695 760 3695 820 3643 790 3695 760
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3695 360}%
\special{pa 3695 420}%
\special{pa 3643 390}%
\special{pa 3695 360}%
\special{fp}%
% CIRCLE 2 1 3 0
% 4 2995 790 2995 590 2795 790 3195 790
% 
\special{pn 8}%
\special{ar 2995 390 200 200  6.2831853 6.5831853}%
\special{ar 2995 390 200 200  6.7631853 7.0631853}%
\special{ar 2995 390 200 200  7.2431853 7.5431853}%
\special{ar 2995 390 200 200  7.7231853 8.0231853}%
\special{ar 2995 390 200 200  8.2031853 8.5031853}%
\special{ar 2995 390 200 200  8.6831853 8.9831853}%
\special{ar 2995 390 200 200  9.1631853 9.4247780}%
% POLYGON 2 0 0 0
% 4 3105 950 3135 898 3165 950 3105 950
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3105 550}%
\special{pa 3135 498}%
\special{pa 3165 550}%
\special{pa 3105 550}%
\special{fp}%
% CIRCLE 2 1 3 0
% 4 3695 790 3695 590 3495 790 3895 790
% 
\special{pn 8}%
\special{ar 3695 390 200 200  6.2831853 6.5831853}%
\special{ar 3695 390 200 200  6.7631853 7.0631853}%
\special{ar 3695 390 200 200  7.2431853 7.5431853}%
\special{ar 3695 390 200 200  7.7231853 8.0231853}%
\special{ar 3695 390 200 200  8.2031853 8.5031853}%
\special{ar 3695 390 200 200  8.6831853 8.9831853}%
\special{ar 3695 390 200 200  9.1631853 9.4247780}%
% POLYGON 2 0 0 0
% 4 3805 950 3835 898 3865 950 3805 950
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3805 550}%
\special{pa 3835 498}%
\special{pa 3865 550}%
\special{pa 3805 550}%
\special{fp}%
% STR 2 0 3 0
% 3 5790 1900 5790 2000 5 0
% (g)
\put(57.9000,-16.0000){\makebox(0,0){(g)}}%
% STR 2 0 3 0
% 3 1615 3225 1615 3325 5 0
% (h)
\put(16.1500,-29.2500){\makebox(0,0){(h)}}%
% DOT 1 0 3 0
% 6 5100 2740 5100 2840 5100 2940 5100 3040 5100 3140 5100 3140
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5100 2340 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 2440 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 2540 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 2640 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 2740 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 2740 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 6 4410 2740 4410 2840 4410 2940 4410 3040 4410 3140 4410 3140
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4410 2340 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4410 2440 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4410 2540 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4410 2640 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4410 2740 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4410 2740 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 6 5800 2560 5800 2660 5800 2760 5800 2860 5800 2960 5800 2960
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5800 2160 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 2260 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 2360 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 2460 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 2560 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 2560 10 10 0  6.28318530717959E+0000}%
% CIRCLE 2 1 3 0
% 4 5100 2550 5100 2350 5100 2350 5100 2350
% 
\special{pn 8}%
\special{ar 5100 2150 200 200  0.0000000 0.3000000}%
\special{ar 5100 2150 200 200  0.4800000 0.7800000}%
\special{ar 5100 2150 200 200  0.9600000 1.2600000}%
\special{ar 5100 2150 200 200  1.4400000 1.7400000}%
\special{ar 5100 2150 200 200  1.9200000 2.2200000}%
\special{ar 5100 2150 200 200  2.4000000 2.7000000}%
\special{ar 5100 2150 200 200  2.8800000 3.1800000}%
\special{ar 5100 2150 200 200  3.3600000 3.6600000}%
\special{ar 5100 2150 200 200  3.8400000 4.1400000}%
\special{ar 5100 2150 200 200  4.3200000 4.6200000}%
\special{ar 5100 2150 200 200  4.8000000 5.1000000}%
\special{ar 5100 2150 200 200  5.2800000 5.5800000}%
\special{ar 5100 2150 200 200  5.7600000 6.0600000}%
\special{ar 5100 2150 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 4410 2540 4410 2340 4410 2340 4410 2340
% 
\special{pn 8}%
\special{ar 4410 2140 200 200  0.0000000 0.3000000}%
\special{ar 4410 2140 200 200  0.4800000 0.7800000}%
\special{ar 4410 2140 200 200  0.9600000 1.2600000}%
\special{ar 4410 2140 200 200  1.4400000 1.7400000}%
\special{ar 4410 2140 200 200  1.9200000 2.2200000}%
\special{ar 4410 2140 200 200  2.4000000 2.7000000}%
\special{ar 4410 2140 200 200  2.8800000 3.1800000}%
\special{ar 4410 2140 200 200  3.3600000 3.6600000}%
\special{ar 4410 2140 200 200  3.8400000 4.1400000}%
\special{ar 4410 2140 200 200  4.3200000 4.6200000}%
\special{ar 4410 2140 200 200  4.8000000 5.1000000}%
\special{ar 4410 2140 200 200  5.2800000 5.5800000}%
\special{ar 4410 2140 200 200  5.7600000 6.0600000}%
\special{ar 4410 2140 200 200  6.2400000 6.2832853}%
% BOX 2 0 2 0
% 2 5770 2580 5830 2520
% 
\special{pn 8}%
\special{sh 0}%
\special{pa 5770 2180}%
\special{pa 5830 2180}%
\special{pa 5830 2120}%
\special{pa 5770 2120}%
\special{pa 5770 2180}%
\special{fp}%
% BOX 2 0 2 0
% 2 4380 2370 4440 2310
% 
\special{pn 8}%
\special{sh 0}%
\special{pa 4380 1970}%
\special{pa 4440 1970}%
\special{pa 4440 1910}%
\special{pa 4380 1910}%
\special{pa 4380 1970}%
\special{fp}%
% BOX 2 0 2 0
% 2 5070 2770 5130 2710
% 
\special{pn 8}%
\special{sh 0}%
\special{pa 5070 2370}%
\special{pa 5130 2370}%
\special{pa 5130 2310}%
\special{pa 5070 2310}%
\special{pa 5070 2370}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 5270 2560 5330 2560 5300 2612 5270 2560
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 5270 2160}%
\special{pa 5330 2160}%
\special{pa 5300 2212}%
\special{pa 5270 2160}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 4580 2550 4640 2550 4610 2602 4580 2550
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 4580 2150}%
\special{pa 4640 2150}%
\special{pa 4610 2202}%
\special{pa 4580 2150}%
\special{fp}%
% STR 2 0 3 0
% 3 4410 3220 4410 3320 5 0
% (l)
\put(44.1000,-29.2000){\makebox(0,0){(l)}}%
% STR 2 0 3 0
% 3 5110 3220 5110 3320 5 0
% (m)
\put(51.1000,-29.2000){\makebox(0,0){(m)}}%
% STR 2 0 3 0
% 3 5810 3220 5810 3320 5 0
% (n)
\put(58.1000,-29.2000){\makebox(0,0){(n)}}%
% CIRCLE 2 1 3 0
% 4 1600 800 1800 800 1800 800 1800 800
% 
\special{pn 8}%
\special{ar 1600 400 200 200  0.0000000 0.3000000}%
\special{ar 1600 400 200 200  0.4800000 0.7800000}%
\special{ar 1600 400 200 200  0.9600000 1.2600000}%
\special{ar 1600 400 200 200  1.4400000 1.7400000}%
\special{ar 1600 400 200 200  1.9200000 2.2200000}%
\special{ar 1600 400 200 200  2.4000000 2.7000000}%
\special{ar 1600 400 200 200  2.8800000 3.1800000}%
\special{ar 1600 400 200 200  3.3600000 3.6600000}%
\special{ar 1600 400 200 200  3.8400000 4.1400000}%
\special{ar 1600 400 200 200  4.3200000 4.6200000}%
\special{ar 1600 400 200 200  4.8000000 5.1000000}%
\special{ar 1600 400 200 200  5.2800000 5.5800000}%
\special{ar 1600 400 200 200  5.7600000 6.0600000}%
\special{ar 1600 400 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 4400 1200 4600 1200 4600 1200 4600 1200
% 
\special{pn 8}%
\special{ar 4400 800 200 200  0.0000000 0.3000000}%
\special{ar 4400 800 200 200  0.4800000 0.7800000}%
\special{ar 4400 800 200 200  0.9600000 1.2600000}%
\special{ar 4400 800 200 200  1.4400000 1.7400000}%
\special{ar 4400 800 200 200  1.9200000 2.2200000}%
\special{ar 4400 800 200 200  2.4000000 2.7000000}%
\special{ar 4400 800 200 200  2.8800000 3.1800000}%
\special{ar 4400 800 200 200  3.3600000 3.6600000}%
\special{ar 4400 800 200 200  3.8400000 4.1400000}%
\special{ar 4400 800 200 200  4.3200000 4.6200000}%
\special{ar 4400 800 200 200  4.8000000 5.1000000}%
\special{ar 4400 800 200 200  5.2800000 5.5800000}%
\special{ar 4400 800 200 200  5.7600000 6.0600000}%
\special{ar 4400 800 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 5800 1200 6000 1200 6000 1200 6000 1200
% 
\special{pn 8}%
\special{ar 5800 800 200 200  0.0000000 0.3000000}%
\special{ar 5800 800 200 200  0.4800000 0.7800000}%
\special{ar 5800 800 200 200  0.9600000 1.2600000}%
\special{ar 5800 800 200 200  1.4400000 1.7400000}%
\special{ar 5800 800 200 200  1.9200000 2.2200000}%
\special{ar 5800 800 200 200  2.4000000 2.7000000}%
\special{ar 5800 800 200 200  2.8800000 3.1800000}%
\special{ar 5800 800 200 200  3.3600000 3.6600000}%
\special{ar 5800 800 200 200  3.8400000 4.1400000}%
\special{ar 5800 800 200 200  4.3200000 4.6200000}%
\special{ar 5800 800 200 200  4.8000000 5.1000000}%
\special{ar 5800 800 200 200  5.2800000 5.5800000}%
\special{ar 5800 800 200 200  5.7600000 6.0600000}%
\special{ar 5800 800 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 1610 2530 1810 2530 1810 2530 1810 2530
% 
\special{pn 8}%
\special{ar 1610 2130 200 200  0.0000000 0.3000000}%
\special{ar 1610 2130 200 200  0.4800000 0.7800000}%
\special{ar 1610 2130 200 200  0.9600000 1.2600000}%
\special{ar 1610 2130 200 200  1.4400000 1.7400000}%
\special{ar 1610 2130 200 200  1.9200000 2.2200000}%
\special{ar 1610 2130 200 200  2.4000000 2.7000000}%
\special{ar 1610 2130 200 200  2.8800000 3.1800000}%
\special{ar 1610 2130 200 200  3.3600000 3.6600000}%
\special{ar 1610 2130 200 200  3.8400000 4.1400000}%
\special{ar 1610 2130 200 200  4.3200000 4.6200000}%
\special{ar 1610 2130 200 200  4.8000000 5.1000000}%
\special{ar 1610 2130 200 200  5.2800000 5.5800000}%
\special{ar 1610 2130 200 200  5.7600000 6.0600000}%
\special{ar 1610 2130 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 2300 800 2500 800 2500 800 2500 800
% 
\special{pn 8}%
\special{ar 2300 400 200 200  0.0000000 0.3000000}%
\special{ar 2300 400 200 200  0.4800000 0.7800000}%
\special{ar 2300 400 200 200  0.9600000 1.2600000}%
\special{ar 2300 400 200 200  1.4400000 1.7400000}%
\special{ar 2300 400 200 200  1.9200000 2.2200000}%
\special{ar 2300 400 200 200  2.4000000 2.7000000}%
\special{ar 2300 400 200 200  2.8800000 3.1800000}%
\special{ar 2300 400 200 200  3.3600000 3.6600000}%
\special{ar 2300 400 200 200  3.8400000 4.1400000}%
\special{ar 2300 400 200 200  4.3200000 4.6200000}%
\special{ar 2300 400 200 200  4.8000000 5.1000000}%
\special{ar 2300 400 200 200  5.2800000 5.5800000}%
\special{ar 2300 400 200 200  5.7600000 6.0600000}%
\special{ar 2300 400 200 200  6.2400000 6.2832853}%
% CIRCLE 2 1 3 0
% 4 5100 1200 5300 1200 5300 1200 5300 1200
% 
\special{pn 8}%
\special{ar 5100 800 200 200  0.0000000 0.3000000}%
\special{ar 5100 800 200 200  0.4800000 0.7800000}%
\special{ar 5100 800 200 200  0.9600000 1.2600000}%
\special{ar 5100 800 200 200  1.4400000 1.7400000}%
\special{ar 5100 800 200 200  1.9200000 2.2200000}%
\special{ar 5100 800 200 200  2.4000000 2.7000000}%
\special{ar 5100 800 200 200  2.8800000 3.1800000}%
\special{ar 5100 800 200 200  3.3600000 3.6600000}%
\special{ar 5100 800 200 200  3.8400000 4.1400000}%
\special{ar 5100 800 200 200  4.3200000 4.6200000}%
\special{ar 5100 800 200 200  4.8000000 5.1000000}%
\special{ar 5100 800 200 200  5.2800000 5.5800000}%
\special{ar 5100 800 200 200  5.7600000 6.0600000}%
\special{ar 5100 800 200 200  6.2400000 6.2832853}%
% DOT 1 2 3 0
% 6 1600 1000 1600 1200 1600 1400 1600 1100 1600 1300 1600 1300
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1600 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1600 800 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1600 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1600 700 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1600 900 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1600 900 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 4400 1390 4400 1590 4400 1790 4400 1490 4400 1690 4400 1690
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4400 990 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4400 1190 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4400 1390 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4400 1090 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4400 1290 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4400 1290 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 5800 1400 5800 1600 5800 1800 5800 1500 5800 1700 5800 1700
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5800 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 1200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 1100 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 1300 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5800 1300 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 1610 2730 1610 2930 1610 3130 1610 2830 1610 3030 1610 3030
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1610 2330 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1610 2530 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1610 2730 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1610 2430 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1610 2630 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1610 2630 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 2300 1000 2300 1200 2300 1400 2300 1100 2300 1300 2300 1300
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2300 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 800 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 700 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 900 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 900 10 10 0  6.28318530717959E+0000}%
% DOT 1 2 3 0
% 6 5100 1400 5100 1600 5100 1800 5100 1500 5100 1700 5100 1700
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5100 1000 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 1200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 1400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 1100 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 1300 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5100 1300 10 10 0  6.28318530717959E+0000}%
% SPLINE 2 0 3 0
% 8 1410 2530 1490 2500 1550 2560 1610 2500 1670 2560 1730 2500 1810 2530 1810 2530
% 
\special{pn 8}%
\special{pa 1410 2130}%
\special{pa 1442 2107}%
\special{pa 1472 2096}%
\special{pa 1498 2107}%
\special{pa 1522 2137}%
\special{pa 1543 2159}%
\special{pa 1565 2149}%
\special{pa 1588 2117}%
\special{pa 1611 2100}%
\special{pa 1634 2119}%
\special{pa 1656 2150}%
\special{pa 1678 2159}%
\special{pa 1700 2135}%
\special{pa 1723 2105}%
\special{pa 1750 2096}%
\special{pa 1780 2108}%
\special{pa 1810 2130}%
\special{sp}%
% DOT 1 0 3 0
% 3 4320 600 4480 600 4480 600
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4320 200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4480 200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4480 200 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 3 4320 1000 4480 1000 4480 1000
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4320 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4480 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4480 600 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 4360 600 4440 600
% 
\special{pn 8}%
\special{pa 4360 200}%
\special{pa 4440 200}%
\special{fp}%
% LINE 2 0 3 0
% 2 4360 1000 4440 1000
% 
\special{pn 8}%
\special{pa 4360 600}%
\special{pa 4440 600}%
\special{fp}%
% DOT 1 0 3 0
% 3 4600 720 4600 880 4600 880
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4600 320 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4600 480 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4600 480 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 4600 760 4600 840
% 
\special{pn 8}%
\special{pa 4600 360}%
\special{pa 4600 440}%
\special{fp}%
% DOT 1 0 3 0
% 3 4200 720 4200 880 4200 880
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4200 320 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4200 480 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4200 480 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 4200 760 4200 840
% 
\special{pn 8}%
\special{pa 4200 360}%
\special{pa 4200 440}%
\special{fp}%
% LINE 2 0 3 0
% 2 4520 620 4580 680
% 
\special{pn 8}%
\special{pa 4520 220}%
\special{pa 4580 280}%
\special{fp}%
% LINE 2 0 3 0
% 2 4220 910 4280 970
% 
\special{pn 8}%
\special{pa 4220 510}%
\special{pa 4280 570}%
\special{fp}%
% LINE 2 0 3 0
% 2 4280 620 4220 680
% 
\special{pn 8}%
\special{pa 4280 220}%
\special{pa 4220 280}%
\special{fp}%
% LINE 2 0 3 0
% 2 4560 920 4500 980
% 
\special{pn 8}%
\special{pa 4560 520}%
\special{pa 4500 580}%
\special{fp}%
% DOT 1 0 3 0
% 3 5020 600 5180 600 5180 600
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5020 200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5180 200 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5180 200 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 5060 600 5140 600
% 
\special{pn 8}%
\special{pa 5060 200}%
\special{pa 5140 200}%
\special{fp}%
% DOT 1 0 3 0
% 3 5300 720 5300 880 5300 880
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5300 320 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5300 480 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5300 480 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 5300 760 5300 840
% 
\special{pn 8}%
\special{pa 5300 360}%
\special{pa 5300 440}%
\special{fp}%
% DOT 1 0 3 0
% 3 4900 720 4900 880 4900 880
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 4900 320 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4900 480 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 4900 480 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 4900 760 4900 840
% 
\special{pn 8}%
\special{pa 4900 360}%
\special{pa 4900 440}%
\special{fp}%
% LINE 2 0 3 0
% 2 5220 620 5280 680
% 
\special{pn 8}%
\special{pa 5220 220}%
\special{pa 5280 280}%
\special{fp}%
% LINE 2 0 3 0
% 2 4920 910 4980 970
% 
\special{pn 8}%
\special{pa 4920 510}%
\special{pa 4980 570}%
\special{fp}%
% LINE 2 0 3 0
% 2 4980 620 4920 680
% 
\special{pn 8}%
\special{pa 4980 220}%
\special{pa 4920 280}%
\special{fp}%
% LINE 2 0 3 0
% 2 5260 920 5200 980
% 
\special{pn 8}%
\special{pa 5260 520}%
\special{pa 5200 580}%
\special{fp}%
% DOT 1 0 3 0
% 3 5020 1000 5180 1000 5180 1000
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 5020 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5180 600 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 5180 600 10 10 0  6.28318530717959E+0000}%
% LINE 2 0 3 0
% 2 5060 1000 5140 1000
% 
\special{pn 8}%
\special{pa 5060 600}%
\special{pa 5140 600}%
\special{fp}%
% SPLINE 2 0 3 0
% 18 5800 1000 5760 900 5650 940 5700 840 5600 800 5700 760 5650 660 5760 700 5800 600 5840 700 5950 660 5900 760 6000 800 5900 840 5950 940 5840 900 5800 1000 5800 1000
% 
\special{pn 8}%
\special{pa 5800 600}%
\special{pa 5796 558}%
\special{pa 5788 523}%
\special{pa 5770 503}%
\special{pa 5738 503}%
\special{pa 5699 518}%
\special{pa 5665 535}%
\special{pa 5650 540}%
\special{pa 5662 523}%
\special{pa 5685 491}%
\special{pa 5702 456}%
\special{pa 5690 428}%
\special{pa 5653 412}%
\special{pa 5615 404}%
\special{pa 5600 400}%
\special{pa 5623 395}%
\special{pa 5663 385}%
\special{pa 5696 367}%
\special{pa 5700 335}%
\special{pa 5680 299}%
\special{pa 5657 270}%
\special{pa 5651 260}%
\special{pa 5672 273}%
\special{pa 5708 294}%
\special{pa 5747 303}%
\special{pa 5775 286}%
\special{pa 5791 247}%
\special{pa 5797 211}%
\special{pa 5801 201}%
\special{pa 5805 226}%
\special{pa 5815 266}%
\special{pa 5836 298}%
\special{pa 5871 301}%
\special{pa 5910 284}%
\special{pa 5941 265}%
\special{pa 5949 261}%
\special{pa 5933 282}%
\special{pa 5909 316}%
\special{pa 5898 351}%
\special{pa 5917 377}%
\special{pa 5956 391}%
\special{pa 5991 397}%
\special{pa 5997 401}%
\special{pa 5968 407}%
\special{pa 5928 418}%
\special{pa 5900 440}%
\special{pa 5904 472}%
\special{pa 5926 507}%
\special{pa 5947 534}%
\special{pa 5946 540}%
\special{pa 5921 528}%
\special{pa 5882 510}%
\special{pa 5845 500}%
\special{pa 5820 510}%
\special{pa 5807 538}%
\special{pa 5802 577}%
\special{pa 5800 600}%
\special{sp}%
% DOT 1 0 3 0
% 5 1450 800 1550 800 1650 800 1750 800 1750 800
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 1450 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1550 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1650 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1750 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 1750 400 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 5 2150 800 2250 800 2350 800 2450 800 2450 800
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2150 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2250 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2350 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2450 400 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2450 400 10 10 0  6.28318530717959E+0000}%
% POLYGON 2 0 0 0
% 4 1600 630 1600 570 1652 600 1600 630
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 1600 230}%
\special{pa 1600 170}%
\special{pa 1652 200}%
\special{pa 1600 230}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 2300 630 2300 570 2352 600 2300 630
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2300 230}%
\special{pa 2300 170}%
\special{pa 2352 200}%
\special{pa 2300 230}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 1600 2360 1600 2300 1652 2330 1600 2360
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 1600 1960}%
\special{pa 1600 1900}%
\special{pa 1652 1930}%
\special{pa 1600 1960}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 2300 770 2300 830 2248 800 2300 770
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2300 370}%
\special{pa 2300 430}%
\special{pa 2248 400}%
\special{pa 2300 370}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 4570 1200 4630 1200 4600 1252 4570 1200
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 4570 800}%
\special{pa 4630 800}%
\special{pa 4600 852}%
\special{pa 4570 800}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 5270 1200 5330 1200 5300 1252 5270 1200
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 5270 800}%
\special{pa 5330 800}%
\special{pa 5300 852}%
\special{pa 5270 800}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 5970 1200 6030 1200 6000 1252 5970 1200
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 5970 800}%
\special{pa 6030 800}%
\special{pa 6000 852}%
\special{pa 5970 800}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 5270 780 5330 780 5300 832 5270 780
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 5270 380}%
\special{pa 5330 380}%
\special{pa 5300 432}%
\special{pa 5270 380}%
\special{fp}%
% STR 2 0 3 0
% 3 1625 1900 1625 2000 5 0
% (a)
\put(16.2500,-16.0000){\makebox(0,0){(a)}}%
% STR 2 0 3 0
% 3 2325 1900 2325 2000 5 0
% (b)
\put(23.2500,-16.0000){\makebox(0,0){(b)}}%
% STR 2 0 3 0
% 3 3030 1885 3030 1985 5 0
% (c)
\put(30.3000,-15.8500){\makebox(0,0){(c)}}%
% STR 2 0 3 0
% 3 3730 1885 3730 1985 5 0
% (d)
\put(37.3000,-15.8500){\makebox(0,0){(d)}}%
% STR 2 0 3 0
% 3 4405 1885 4405 1985 5 0
% (e)
\put(44.0500,-15.8500){\makebox(0,0){(e)}}%
% STR 2 0 3 0
% 3 5105 1885 5105 1985 5 0
% (f)
\put(51.0500,-15.8500){\makebox(0,0){(f)}}%
% STR 2 0 3 0
% 3 2300 610 2300 710 5 0
% $\beta$
\put(23.0000,-3.1000){\makebox(0,0){$\beta$}}%
% STR 2 0 3 0
% 3 3000 590 3000 690 5 0
% $c$
\put(30.0000,-2.9000){\makebox(0,0){$c$}}%
% STR 2 0 3 0
% 3 3710 590 3710 690 5 0
% $e$
\put(37.1000,-2.9000){\makebox(0,0){$e$}}%
% STR 2 0 3 0
% 3 4720 690 4720 790 5 0
% $\sigma$
\put(47.2000,-3.9000){\makebox(0,0){$\sigma$}}%
% STR 2 0 3 0
% 3 5440 690 5440 790 5 0
% $\tau$
\put(54.4000,-3.9000){\makebox(0,0){$\tau$}}%
% STR 2 0 3 0
% 3 6100 700 6100 800 5 0
% $A_\mu$
\put(61.0000,-4.0000){\makebox(0,0){$A_\mu$}}%
% STR 2 0 3 0
% 3 1610 610 1610 710 5 0
% $\alpha$
\put(16.1000,-3.1000){\makebox(0,0){$\alpha$}}%
% DOT 1 0 3 0
% 6 2300 2714 2300 2814 2300 2914 2300 3014 2300 3114 2300 3114
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 2300 2314 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 2414 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 2514 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 2614 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 2714 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 2300 2714 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 6 3000 2714 3000 2814 3000 2914 3000 3014 3000 3114 3000 3114
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 3000 2314 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3000 2414 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3000 2514 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3000 2614 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3000 2714 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3000 2714 10 10 0  6.28318530717959E+0000}%
% DOT 1 0 3 0
% 6 3700 2714 3700 2814 3700 2914 3700 3014 3700 3114 3700 3114
% 
\special{pn 13}%
\special{sh 1}%
\special{ar 3700 2314 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3700 2414 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3700 2514 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3700 2614 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3700 2714 10 10 0  6.28318530717959E+0000}%
\special{sh 1}%
\special{ar 3700 2714 10 10 0  6.28318530717959E+0000}%
% CIRCLE 2 1 3 0
% 4 2300 2514 2300 2314 2100 2514 2500 2514
% 
\special{pn 8}%
\special{ar 2300 2114 200 200  6.2831853 6.5831853}%
\special{ar 2300 2114 200 200  6.7631853 7.0631853}%
\special{ar 2300 2114 200 200  7.2431853 7.5431853}%
\special{ar 2300 2114 200 200  7.7231853 8.0231853}%
\special{ar 2300 2114 200 200  8.2031853 8.5031853}%
\special{ar 2300 2114 200 200  8.6831853 8.9831853}%
\special{ar 2300 2114 200 200  9.1631853 9.4247780}%
% POLYGON 2 0 0 0
% 4 2410 2674 2440 2622 2470 2674 2410 2674
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 2410 2274}%
\special{pa 2440 2222}%
\special{pa 2470 2274}%
\special{pa 2410 2274}%
\special{fp}%
% POLYGON 2 0 0 0
% 4 3110 2674 3140 2622 3170 2674 3110 2674
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3110 2274}%
\special{pa 3140 2222}%
\special{pa 3170 2274}%
\special{pa 3110 2274}%
\special{fp}%
% CIRCLE 2 1 3 0
% 4 3700 2514 3700 2314 3500 2514 3900 2514
% 
\special{pn 8}%
\special{ar 3700 2114 200 200  6.2831853 6.5831853}%
\special{ar 3700 2114 200 200  6.7631853 7.0631853}%
\special{ar 3700 2114 200 200  7.2431853 7.5431853}%
\special{ar 3700 2114 200 200  7.7231853 8.0231853}%
\special{ar 3700 2114 200 200  8.2031853 8.5031853}%
\special{ar 3700 2114 200 200  8.6831853 8.9831853}%
\special{ar 3700 2114 200 200  9.1631853 9.4247780}%
% POLYGON 2 0 0 0
% 4 3810 2674 3840 2622 3870 2674 3810 2674
% 
\special{pn 8}%
\special{sh 0.600}%
\special{pa 3810 2274}%
\special{pa 3840 2222}%
\special{pa 3870 2274}%
\special{pa 3810 2274}%
\special{fp}%
% POLYGON 2 0 0 0
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\title{Cancellation of UV Divergences in the ${\cal N}=4$ SUSY Nonlinear Sigma Model in Three Dimensions}
\author{Takeo Inami,
Yorinori Saito
and
Masayoshi Yamamoto\\
\it Department of Physics,
Faculty of Science and Engineering\\
\it Chuo University,
1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan}
\date{\,}
\begin{document}
\maketitle


\begin{center}
\begin{abstract}We study the UV properties of the three-dimensional ${\cal N}=4$ SUSY nonlinear sigma model whose target space is $T^*(CP^{N-1})$ (the cotangent bundle of $CP^{N-1}$) to higher orders in the $1/N$ expansion. We calculate the $\beta$-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.
\end{abstract}
\end{center}

\newpage

\section{Introduction}
Three-dimensional nonlinear sigma models have special properties regarding UV divergences. They are non-renormalizable theories in the sense of perturbation expansion, but they are renormalizable in the $1/N$ expansion \cite{Arefeva, Vasilev}. The three-dimensional $O(N)$ and $CP^{N-1}$ nonlinear sigma models were studied to next-to-leading order in $1/N$ and their $\beta$-functions were determined to this order \cite{Rosenstein, Gracey, Cant}. 

An important feature of SUSY field theories is weaker quantum corrections, particularly UV divergences in the perturbation expansion. We want to pose the question: ``Do SUSY field theories have this feature in the $1/N$ expansion? Does the model with higher ${\cal N}$ extended SUSY have better UV property?''  We address ourselves to these questions in extended SUSY nonlinear sigma models in three dimensions.

Some works have been made in this direction. In the ${\cal N}=1$ SUSY $O(N)$ nonlinear sigma model in three dimensions, the next-to-leading order term in the $\beta$-function turned out to be absent modulo power divergences in the $1/N$ expansion \cite{Koures} and in the critical exponent technique \cite{Gracey2}. In the ${\cal N}=2$ SUSY $CP^{N-1}$ model in three dimensions, the next-to-leading order term in the $\beta$-function was found to vanish \cite{Inami, Gracey3}. In the ${\cal N}=4$ SUSY nonlinear sigma model in three dimensions whose target space is $T^*(CP^{N-1})$ (the cotangent bundle of $CP^{N-1}$), the $\beta$-function was found to receive no quantum corrections at leading order \cite{Inami2}. Curiously, these results in low orders of $1/N$ are reminiscent of the UV properties in perturbation of ${\cal N}=1,2$ and $4$ SUSY gauge theories in four dimensions.

We have initiated a study of the UV properties of the ${\cal N}=4$ SUSY $T^*(CP^{N-1})$ model in three dimensions in higher orders of the $1/N$ expansion. Nonlinear sigma models in three dimensions are plagued by a number of power divergences in the cutoff $\Lambda$. We investigate how such UV divergences may combine to cancel out in the model. To this end we use the cutoff regularization. In this letter we present the result of the computation of the $\beta$-function to next-to-leading order in $1/N$. We have previously shown that the $\beta$-function at leading order receives no quantum corrections in the saddle point evaluation \cite{Inami2}. We examine whether this remarkable property will persist at higher orders.

\section{The Model}

We consider the ${\cal N}=4$ SUSY $T^*(CP^{N-1})$ model in three dimensions \cite{Inami2}. The model can be constructed from the ${\cal N}=2$ model in four dimensions \cite{Curtright} by dimensional reduction. We follow \cite{Curtright} and use the component language. The model consists of $2N$ complex scalar fields $\phi^\alpha_i (x)$ ($i=1,2$; $\alpha=1,\dots,N$), $2N$ Dirac fields $\psi^\alpha_i (x)$ (the superpartners of $\phi^\alpha_i$) and  auxiliary fields $\sigma (x)$ (real scalar), $\tau (x)$ (complex scalar), $A_\mu (x)$ ($U(1)$ vector). The Lagrangian is given by \cite{Inami2}
\beqa
{\cal L}_1&=&\overline{D_\mu\phi^\alpha_i}D_\mu\phi^\alpha_i
+i\bar{\psi}^\alpha_i\gamma_\mu D_\mu\psi^\alpha_i
-\tau\bar{\psi}^\alpha_1\psi^\alpha_2-\bar{\tau}\bar{\psi}^\alpha_2\psi^\alpha_1
\nonumber\\
&&+\sigma(\bar{\psi}^\alpha_1\psi^\alpha_1-\bar{\psi}^\alpha_2 \psi^\alpha_2)+(\bar{\tau}\tau+\sigma^2)\bar{\phi}^\alpha_i\phi^\alpha_i,
\label{3daction}
\eeqa
with the constraints
\beqa
&&\bar{\phi}^\alpha_1 \phi^\alpha_1-\bar{\phi}^\alpha_2\phi^\alpha_2=N/g,
~~~\bar{\phi}^\alpha_1\phi^\alpha_2=0,
\label{3dconstraint1}\\
&&\bar{\phi}^\alpha_1\psi^\alpha_1-i\phi^\alpha_2\psi^{\alpha *}_2=0,
~~~\bar{\phi}^\alpha_1\psi^\alpha_2+i\phi^\alpha_2\psi^{\alpha *}_1=0.
\label{3dconstraint2}
\eeqa
We use the Euclidean metric and $D_\mu=\partial_\mu+iA_\mu$ ($\mu=1,2,3$). The symbol $\gamma^\mu$ is the Dirac matrices in three dimensions. They are given by  $\gamma^1=i\sigma_2$, $\gamma^2=i\sigma_3$ and $\gamma^3=i\sigma_1$. Simple dimensional reduction assures that the model (\ref{3daction}) inherits  ${\cal N}=4$ SUSY from the four-dimensional ${\cal N}=2$ SUSY model \cite{Curtright}.

The constraints (\ref{3dconstraint1}) and (\ref{3dconstraint2}) may be expressed as $\delta$-functionals. This introduces a real scalar $\alpha (x)$, a complex scalar $\beta (x)$ and two complex spinors $c (x)$ and $e (x)$ as the Lagrange multiplier fields:
\beqa
{\cal L}&=&{\cal L}_1-\alpha( \bar{\phi}^\alpha_{1}\phi^\alpha_{1}-\bar{\phi}^\alpha_{2}\phi^\alpha_{2}-N/g )\nonumber\\
&&-\beta\bar{\phi}^\alpha_{1}\phi^\alpha_{2}-\bar{\beta}\bar{\phi}^\alpha_{2}\phi^\alpha_{1}
\nonumber\\
&&+\bar{\phi}^\alpha_{1}\bar{c}\psi^\alpha_{1}+\phi^\alpha_{1}\bar{\psi}^\alpha_{1} c+i\bar{\phi}^\alpha_{2}\bar{c}^* \psi^\alpha_{2}-i\phi^\alpha_{2}\bar{\psi}^\alpha_{2} c^*
\nonumber\\
&&+\bar{\phi}^\alpha_{1}\bar{e}\psi^\alpha_{2}+\phi^\alpha_{1}\bar{\psi}^\alpha_{2} e-i\bar{\phi}^\alpha_{2}\bar{e}^* \psi^\alpha_{1}
+i\phi^\alpha_{2}\bar{\psi}^\alpha_{1} e^*.
\label{eq:lag0}
\eeqa
The sets of the fields $(A_\mu, c, \sigma, \alpha)$ and $(\tau, e, \beta)$ are the components of the ${\cal N}=2$  $U(1)$ vector multiplet in the Wess-Zumino gauge and the ${\cal N}=2$  Lagrange multiplier multiplet respectively, which are obtained by dimensional reduction of the four-dimensional ${\cal N}=2$ model in the superfield formulation \cite{Rocek}.

The vacuum of the model is determined by the expectation values of the scalar fields $\phi_i^\alpha$. Taking account of the constraints (\ref{3dconstraint1}), we set
\beq
\langle\stackrel{\rightarrow}{\phi_1}\rangle=(0,\cdots,\sqrt{N}r),~~~\langle\stackrel{\rightarrow}{\phi_2}\rangle=(0,\cdots,\sqrt{N}s,0). 
\eeq
The values of $r$ and $s$ are fixed from the saddle point conditions. Because of the constraints (\ref{3dconstraint1}), only the broken $SU(N)$ phase is allowed. The vacuum expectation values $r$ and $s$ are related to the coupling constant as $r^2-s^2=1/g$. We study the UV properties of the model by setting $s=0$. We should obtain the same result regarding the UV property of the model for other values of $r$ and $s$. Performing the shift
\beq
\phi^N_1\to\phi^N_1+\sqrt{N}r,
\label{phishift}
\eeq
in (\ref{eq:lag0}), we obtain the Lagrangian
\beqa
{\cal L}^{\prime}&=&\overline{\phi_{i}^\alpha}( -\partial^2-iA_{\mu} \stackrel{\leftrightarrow}{\partial_\mu}+A^2)\phi_{i}^\alpha+(\bar{\tau}\tau+\sigma^2)\bar{\phi}^\alpha_{i}\phi^\alpha_{i}
\nonumber\\
&&-\beta\bar{\phi}^\alpha_{1}\phi^\alpha_{2}-\bar{\beta}\bar{\phi}^\alpha_{2}\phi^\alpha_{1}-\alpha(\bar{\phi}^\alpha_{1}\phi^\alpha_{1}-\bar{\phi}^\alpha_{2}\phi^\alpha_{2}-N/g)
\nonumber\\
&&+\overline{\psi}_{i}^\alpha\left( i\ooalign{\hfil/\hfil\crcr$\partial$}-\ooalign{\hfil/\hfil\crcr$A$}\right)\psi_{i}^\alpha-\tau\bar{\psi}^\alpha_{1}\psi^\alpha_{2}-\bar{\tau}\bar{\psi}^\alpha_{2}\psi^\alpha_{1}+\sigma(\bar{\psi}^\alpha_{1}\psi^\alpha_{1}-\bar{\psi}^\alpha_{2}\psi^\alpha_{2})
\nonumber\\
&&+\bar{\phi}^\alpha_{1}\bar{c}\psi^\alpha_{1}+\phi^\alpha_{1}\bar{\psi}^\alpha_{1} c+i\bar{\phi}^\alpha_{2}\bar{c}^* \psi^\alpha_{2}-i\phi^\alpha_{2}\bar{\psi}^\alpha_{2} c^*
\nonumber\\
&&+\bar{\phi}^\alpha_{1}\bar{e}\psi^\alpha_{2}+\phi^\alpha_{1}\bar{\psi}^\alpha_{2} e
-i\bar{\phi}^\alpha_{2}\bar{e}^*\psi^\alpha_{1}+i\phi^\alpha_{2}\bar{\psi}^\alpha_{1} e^*\nonumber\\
&&+N r^2 (A^2+\bar{\tau}\tau+\sigma^2-\alpha)
\nonumber\\
&&+\sqrt{N}\bar{r}(-i\partial^\mu A_{\mu}+A^2+\bar{\tau}\tau+\sigma^2-\alpha)\phi^N_{1}\nonumber\\
&&+\sqrt{N}r \bar{\phi}^N_{1}(i\partial^\mu A_{\mu}+A^2+\bar{\tau}\tau+\sigma^2-\alpha)
\nonumber\\
&&+\sqrt{N}(r\beta\phi^N_{2}+\bar{r}\bar{\beta}\bar{\phi}^N_{2}+\bar{r}\bar{c}\psi^N_{1}+r\bar{\psi}^N_{1} c+\bar{r}\bar{e}\psi^N_{2}+r\bar{\psi}^N_{2} e).\label{eq:lag1}
\eeqa
The prescription of computing quantum corrections in the $1/N$ expansion is the same as that in the $CP^{N-1}$ model \cite{Arefeva2}. We need the effective propagators of the auxiliary fields. They are given by \cite{Inami2}
\beqa
&&D^A_{\mu\nu}(p)=\frac{1}{N}\frac{4}{\sqrt{p^2}+8 r^2}
\left(\delta_{\mu\nu}-\frac{p_\mu p_\nu}{p^2}\right),
\nonumber\\
&&D^\sigma(p)=\frac{1}{N}\frac{4}{\sqrt{p^2}+8 r^2},
~~~D^\tau(p)=\frac{1}{N}\frac{8}{\sqrt{p^2}+8 r^2},
\nonumber\\
&&D^\alpha(p)=-\frac{1}{N}\frac{4p^2}{\sqrt{p^2}+8 r^2},
~~~D^\beta(p)=-\frac{1}{N}\frac{8p^2}{\sqrt{p^2}+8 r^2},
\nonumber\\
&&D^c(p)=\frac{1}{N}\frac{8p\!\!\!/}{\sqrt{p^2}+8 r^2},
~~~D^e(p)=\frac{1}{N}\frac{8p\!\!\!/}{\sqrt{p^2}+8 r^2}.
\label{propagator}
\eeqa
We have used the Landau gauge in deriving $D^A_{\mu\nu} (p)$. 



\section{The $\beta$-Function}
The bare quantities denoted by the subscript 0 are related to renormalized quantities by 
\beqa
&&\phi_{i,0}=(Z_{\phi i})^{1/2} \phi_{i},
~~~\psi_{i,0}=(Z_{\psi i})^{1/2} \psi_{i},
~~~g_{0}=Z_g g \label{g}\\
&&\varphi_{0}=Z_\varphi \varphi,~~~\varphi=\alpha, \beta, \sigma, \tau, A_\mu, c, e.
\eeqa
We decompose the bare Lagrangian ${\cal L}_0$ into the renormalized part ${\cal L}$ and the counterterm  Lagrangian ${\cal L}_{\rm CT}$, ${\cal L}_0={\cal L}+{\cal L}_{\rm CT}$. ${\cal L}_0$ and ${\cal L}$ are written in terms of the bare and renormalized quantities, respectively. ${\cal L}_0$ is exactly of the same form as ${\cal L}$. ${\cal L}_{\rm CT}$ is designed to eliminate all UV divergences in n-point functions due to loop effects. Because of the shift (\ref{phishift}), it is given by
\beqa
{\cal L}_{\rm CT}^{\prime}&=&-C_1\phi_1\partial^2\phi_1-C_2\alpha(\overline{\phi}_1\phi_1+Nr^2)+C_g \alpha N/g \nonumber \\
&&+C_3\overline{\psi}_1 i\ooalign{\hfil/\hfil\crcr$\partial$}\psi_1+C_4\sigma\overline{\psi}_1\psi_1+\cdots,
\eeqa
where
\beqa
&&C_1=Z_{\phi 1}-1,~~~C_2=Z_{\alpha} Z_{\phi 1}-1,~~~C_g=Z_{\alpha}Z_{g}^{-1}-1,\\
&&C_3=Z_{\psi 1}-1,~~~C_4=Z_{\sigma} Z_{\psi 1}-1,~~~\cdots.\label{zfac}
\eeqa
The $Z$ and $C$ factors are expanded in $1/N$ as $Z=Z^{(0)}+Z^{(1)}+\cdots$ and $C=C^{(0)}+C^{(1)}+\cdots$.

Before discussing the main result of our study, we summarize the result in leading order \cite{Inami2}. There are only a few kinds of loop diagrams in leading order: the tadpole, self-energy and three-point vertex function of the auxiliary fields (without containing $\phi_i$ and $\psi_i$). We are concerned with these diagrams.

$Z_g^{(0)}$ can be obtained by computing the one loop $\alpha$-tadpole contributing to the one-point vertex function ${\mit\Gamma}_{\alpha}$. We find from (\ref{eq:lag1}) that $\phi_1$ and $\phi_2$ loops contribute to this diagram. Since the $\phi_1$ and $\phi_2$ modes contribute with opposite signs, this diagram is zero. This cancellation mechanism of UV divergences is the same as that of the two-dimensional ${\cal N}=4$ SUSY $T^*(CP^{N-1})$ model in the usual perturbation expansion \cite{Curtright}. The three-point vertex function of the auxiliary fields vanish identically as in the $CP^{N-1}$ model \cite{Arefeva2} and the four-fermion model \cite{Rosenstein2} in three dimensions. The same argument holds for the $\sigma$-tadpole \cite{Rosenstein2}.

In fact, the leading-order tadpole diagrams have already been accounted for by the saddle point conditions and so we need not discuss them except to say that these tadpole diagrams should be considered illegal as subdiagrams. Likewise, the self-energy diagrams of the auxiliary fields are also illegal subdiagrams because they are taken into account by the effective propagators (\ref{propagator}) and are all finite. 

Therefore, the model is finite to leading order in $1/N$:
\beq
Z^{(0)}=1,
\eeq
for all factors. In particular, it implies that the $\beta$-function receives no quantum corrections at leading order. However the $\beta$-function receives the trivial tree level contribution; the dimensionless coupling constant ${\tilde g} =\mu g$ (the renormalization scale $\mu$ is of dimension one) depends on $\mu$ at tree level. The $\beta$-function at leading order is therefore given by
\begin{eqnarray}
\beta^{(0)}({\tilde g})={\tilde g}.
\end{eqnarray}


\begin{figure}[t]
\hspace*{20mm}
\vspace*{-14mm}
\input{figs.tex}
\caption{Next-to-leading order diagrams contributing to renormalization of $\phi_1$. We denote the propagators of $\phi$ and $\psi$ by dashed and thin solid lines, respectively.}
\label{self}
\end{figure}


We now proceed to next-to-leading order in $1/N$. We have calculated the next-to-leading order corrections to the self-energies of bosons $\phi_i$ and fermions $\psi_i$  and those to the three-point vertex functions ${\mit\Gamma}_{\alpha \bar{\phi}\phi}$ and ${\mit\Gamma}_{\sigma \bar{\psi}\psi}$. Next-to-leading order diagrams contributing to renormalization of $\phi_1$ are shown in Fig.~\ref{self}. These self-energy diagrams contain UV power divergences, but they cancel out in the sum of all diagrams. This is  because the power-divergent terms cancel between the loops of bosons and fermions of the same multiplet due to SUSY. The two loop diagrams contributing to ${\mit\Gamma}_{\alpha \bar{\phi}\phi}$ (${\mit\Gamma}_{\sigma \bar{\psi}\psi}$) also contain UV power divergences. We find from (\ref{eq:lag1}) that $\phi_1$ ($\psi_1$)  and $\phi_2$ ($\psi_2$) loops contribute to these diagrams. Since the $\phi_1$ ($\psi_1$) and $\phi_2$ ($\psi_2$) modes contribute with opposite signs, the each of these diagrams is zero. The remaining logarithmic divergences are removed by the $Z$ factors in next-to-leading order. Therefore we obtain
\beq
Z_{\phi i}^{(1)}=-{2\over N\pi^2}\ln {\Lambda \over \mu},~~~Z_{\psi i}^{(1)}=-{6\over N\pi^2}\ln {\Lambda \over \mu},~~~Z_{\alpha}^{(1)}=Z_{\sigma}^{(1)}=0.\label{zfac2}
\eeq

The boson and fermion wave-function renormalization constants $Z_\phi$ and $Z_\psi$ should be the same in a manifestly SUSY calculation scheme.  $Z_\phi^{(1)}$ and $Z_\psi^{(1)}$ we have obtained turn out to be unequal. We can think of two possible causes for this disagreement. i) We have used the component language taking the Wess-Zumino gauge for the $U(1)$ vector multiplet. Supersymmetry is broken by this choice. The disagreement of the boson and fermion $Z$ factors have been noted in the perturbative calculation in the SUSY Yang-Mills theory in the Wess-Zumino gauge \cite{Jones}. ii) The momentum cut-off regularization is likely to break SUSY due to asymmetric treatment of boson and fermion loop momenta \cite{Inami3}.
\begin{figure}[t]
\hspace*{15mm}
\vspace*{3mm}
\input{figt.tex}
\caption{Next-to-leading order diagrams of the $\alpha$-tadpole. The squares represent counterterm vertices.}
\label{Feynman}
\end{figure}

Next-to-leading order diagrams of the $\alpha$-tadpole ${\mit\Gamma}_{\alpha}$ are shown in Fig.~\ref{Feynman}. Figs.~2l-2n are counterterm diagrams. These diagrams receive the following contributions:
\begin{eqnarray}
&&{\mit \Gamma}_{\alpha, 2{\rm l}}=-\Delta Z_{\phi 1}^{(1)}+\Delta Z_{\phi 2}^{(1)},  \\
&&{\mit\Gamma}_{\alpha, 2{\rm m}}=\Delta (Z_{\phi 1}^{(1)}+Z_\alpha^{(1)})-\Delta (Z_{\phi 2}^{(1)}+Z_\alpha^{(1)}),\\
&&{\mit\Gamma}_{\alpha, 2{\rm n}}=Nr^2(Z_{\phi 1}^{(1)}+Z_\alpha^{(1)})-N ((Z_g^{-1})^{(1)}+Z_\alpha^{(1)})/g,
\end{eqnarray}
where
\begin{eqnarray}
\Delta=\int {d^3 p\over (2\pi)^3}{N \over p^2}.
\end{eqnarray}
The sum of Figs.~2l and 2m is zero. From the $Z$ factors (\ref{zfac2}), we find
\begin{eqnarray}
{\mit \Gamma}_{\alpha, 2{\rm n}}=-{2r^2\over \pi^2}\ln {\Lambda \over \mu}-{N\over g}Z_g^{(1)}.\label{coun}
\end{eqnarray}
Fig.~2k and the sum of Figs.~2i and 2j are
\begin{eqnarray}
{\mit \Gamma}_{\alpha, 2{\rm k}}=0,~~~{\mit \Gamma}_{\alpha, 2{\rm i}}+{\mit \Gamma}_{\alpha, 2{\rm j}}={2r^2\over \pi^2}\ln {\Lambda \over \mu}.
\end{eqnarray}
We find that this logarithmic divergence is canceled by the first term in the counterterm (\ref{coun}). Thus $Z_g^{(1)}$ can be obtained by computing Figs.~2a-2h. For Fig.~2a we obtain
\begin{eqnarray}
{\mit \Gamma}_{\alpha, 2{\rm a}}={\mit \Gamma}_{\alpha, 2{\rm a}}^{(\phi 1\,{\rm mode})}+{\mit \Gamma}_{\alpha, 2{\rm a}}^{(\phi 2\,{\rm mode})}=0,
\end{eqnarray}
because
\begin{eqnarray}
{\mit \Gamma}_{\alpha, 2{\rm a}}^{(\phi 1\,{\rm mode})}=-{\mit \Gamma}_{\alpha, 2{\rm a}}^{(\phi 2\,{\rm mode})}=\int {d^3 p\over (2\pi)^3}\int {d^3 k\over (2\pi)^3}D^\alpha(p){N \over k^4(p+k)^2}.
\end{eqnarray}
For the same reason, we have found that the each of Figs.~2b-2h is zero. Finally we obtain
\begin{eqnarray}
Z_{g}^{(1)}=0.
\end{eqnarray}
This implies that the $\beta$-function receives no contributions at next-to-leading order:
\begin{eqnarray}
\beta^{(1)}({\tilde g})=0.
\end{eqnarray}


\section{Discussion}
We have shown that the $\beta$-function in the ${\cal N}=4$ SUSY $T^*(CP^{N-1})$ model in three dimensions receives no quantum corrections to leading and next-to-leading orders. There is a theorem that the $\beta$-function in leading and next-to-leading orders has renormalization scheme independent meaning in the usual perturbation expansion \cite{Gross}. In $1/N$ expansion, however, the $\beta$-function will not probably have this feature. It is an important question whether the absence of non-leading corrections to the $\beta$-function persists to all orders in $1/N$. We need to make use of the superfield formulation in order to handle the problem. For instance, in perturbation expansion the two-dimensional ${\cal N}=4$ SUSY nonlinear sigma models were found to be finite to all orders using a general argument combining the background field method and differential geometry in the superfield formulation \cite{Alvarez}. In the $1/N$ expansion, we already know that the two-dimensional ${\cal N}=4$ SUSY  $T^*(CP^{N-1})$ model should be finite to leading order in the superfield formulation \cite{Rocek}. 


\section*{Acknowledgements}
We would like to thank M. Sakamoto for a careful reading of the manuscript and enlightening discussion of the dependence of the $Z$ factors and the $\beta$-function on the scheme. This work is supported partially by the Grants in Aid of Ministry of Education, Culture and Science (Priority Area B "Supersymmetry and Unified Theory" and Basic Research C). M. Y. was supported by a Research Assistantship of Chuo University.




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\end{document}
