%grids.tex for include  - Version 11-16-2021
%Code for the following definitions
%\include{grids}
%\polar
%\grid
%\smallGrid
%\firstQuad
%\gridNoTicks
%\trigGraph
%\R, \N \*
%
\def\R{{\mathbb{R}}}
\def\Z{{\mathbb{Z}}}
\def\N{{\mathbb{N}}}
\def\*{{^{\circ}}}

%firstquad
\def\firstQuad{{
%quad  was already used for the cases statement
\ifx\JPicScale\undefined\def\JPicScale{1.4}\fi
\unitlength \JPicScale mm
\begin{picture}(55,55)(0,0)
\linethickness{0.3mm}
\put(0,5){\line(1,0){55}}
\put(55,5){\vector(1,0){0.12}}
\linethickness{0.3mm}
\put(0,5){\line(0,1){50}}
\put(0,55){\vector(0,1){0.12}}
\scriptsize
% x axis lables
\put(5,3){\makebox(0,0)[cc]{$1$}}
\put(10,3){\makebox(0,0)[cc]{$2$}}
\put(15,3){\makebox(0,0)[cc]{$3$}}
\put(20,3){\makebox(0,0)[cc]{$4$}}
\put(25,3){\makebox(0,0)[cc]{$5$}}
\put(30,3){\makebox(0,0)[cc]{$6$}}
\put(35,3){\makebox(0,0)[cc]{$7$}}
\put(40,3){\makebox(0,0)[cc]{$8$}}
\put(45,3){\makebox(0,0)[cc]{$9$}}
\put(50,3){\makebox(0,0)[cc]{$10$}}
%y axis labels
\put(-2,10){\makebox(0,0)[cc]{$1$}}
\put(-2,15){\makebox(0,0)[cc]{$2$}}
\put(-2,20){\makebox(0,0)[cc]{$3$}}
\put(-2,25){\makebox(0,0)[cc]{$4$}}
\put(-2,30){\makebox(0,0)[cc]{$5$}}
\put(-2,35){\makebox(0,0)[cc]{$6$}}
\put(-2,40){\makebox(0,0)[cc]{$7$}}
\put(-2,45){\makebox(0,0)[cc]{$8$}}
\put(-2,50){\makebox(0,0)[cc]{$9$}}
\put(-2,55){\makebox(0,0)[cc]{$10$}}
\linethickness{0.3mm}
\put(5,4){\line(0,1){2}}
\put(10,4){\line(0,1){2}}
\put(15,4){\line(0,1){2}}
\put(20,4){\line(0,1){2}}
\put(25,4){\line(0,1){2}}
\put(30,4){\line(0,1){2}}
\put(35,4){\line(0,1){2}}
\put(40,4){\line(0,1){2}}
\put(45,4){\line(0,1){2}}
\put(50,4){\line(0,1){2}}
\put(-1,10){\line(1,0){2}}
\put(-1,15){\line(1,0){2}}
\put(-1,20){\line(1,0){2}}
\put(-1,25){\line(1,0){2}}
\put(-1,30){\line(1,0){2}}
\put(-1,35){\line(1,0){2}}
\put(-1,40){\line(1,0){2}}
\put(-1,45){\line(1,0){2}}
\put(-1,50){\line(1,0){2}}
\end{picture}

}}


%\smallGrid
\def\smallGrid{{%
\ifx\JPicScale\undefined\def\JPicScale{1.7}\fi
\unitlength \JPicScale mm\begin{picture}(40,40)(0,0)
%axes
%axes
\linethickness{0.3mm}
\put(0,20){\line(1,0){40}}
\put(40,20){\vector(1,0){0.12}}
\linethickness{0.3mm}
\put(20,0){\line(0,1){40}}
\put(20,40){\vector(0,1){0.12}}
%labels
\scriptsize
\put(0,19){\makebox(0,0)[cc]{$-5$}}
\put(4,19){\makebox(0,0)[cc]{$-4$}}
\put(8,19){\makebox(0,0)[cc]{$-3$}}
\put(12,19){\makebox(0,0)[cc]{$-2$}}
\put(16,19){\makebox(0,0)[cc]{$-1$}}
\put(24,19){\makebox(0,0)[cc]{$1$}}
\put(28,19){\makebox(0,0)[cc]{$2$}}
\put(32,19){\makebox(0,0)[cc]{$3$}}
\put(36,19){\makebox(0,0)[cc]{$4$}}
\put(40,19){\makebox(0,0)[cc]{$5$}}

\put(19,0){\makebox(0,0)[cc]{$-5$}}
\put(19,4){\makebox(0,0)[cc]{$-4$}}
\put(19,8){\makebox(0,0)[cc]{$-3$}}
\put(19,12){\makebox(0,0)[cc]{$-2$}}
\put(19,16){\makebox(0,0)[cc]{$-1$}}
\put(19,24){\makebox(0,0)[cc]{$1$}}
\put(19,28){\makebox(0,0)[cc]{$2$}}
\put(19,32){\makebox(0,0)[cc]{$3$}}
\put(19,36){\makebox(0,0)[cc]{$4$}}
\put(19,40){\makebox(0,0)[cc]{$5$}}


%dashed line grid
\linethickness{0.15mm}
\multiput(0,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(2,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(4,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(6,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(8,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(10,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(12,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(14,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(16,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(18,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(22,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(24,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(26,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(28,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(30,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(32,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(34,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(36,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(38,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(40,0)(0,2.00){20}{\line(0,1){0.1}}

\linethickness{0.15mm}
\multiput(0,0)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,2)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,4)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,6)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,8)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,10)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,12)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,14)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,16)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,18)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,22)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,24)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,26)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,28)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,30)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,32)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,34)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,36)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,38)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,40)(2.00,0){20}{\line(1,0){0.1}}

%tick marks x axis 
\linethickness{0.2mm}
\put(0,19.5){\line(0,1){1}}
%\put(2,19.5){\line(0,1){1}}
\put(4,19.5){\line(0,1){1}}
%\put(6,19.5){\line(0,1){1}}
\put(8,19.5){\line(0,1){1}}
%\put(10,19.5){\line(0,1){1}}
\put(12,19.5){\line(0,1){1}}
%\put(14,19.5){\line(0,1){1}}
\put(16,19.5){\line(0,1){1}}
%\put(18,19.5){\line(0,1){1}}
%\put(22,19.5){\line(0,1){1}}
\put(24,19.5){\line(0,1){1}}
%\put(26,19.5){\line(0,1){1}}
\put(28,19.5){\line(0,1){1}}
%\put(30,19.5){\line(0,1){1}}
\put(32,19.5){\line(0,1){1}}
%\put(34,19.5){\line(0,1){1}}
\put(36,19.5){\line(0,1){1}}
%\put(38,19.5){\line(0,1){1}}


%tick marks y axis
\linethickness{0.2mm}
\put(19.5,0){\line(1,0){1}}
%\put(19.5,2){\line(1,0){1}}
\put(19.5,4){\line(1,0){1}}
%\put(19.5,6){\line(1,0){1}}
\put(19.5,8){\line(1,0){1}}
%\put(19.5,10){\line(1,0){1}}
\put(19.5,12){\line(1,0){1}}
%\put(19.5,14){\line(1,0){1}}
\put(19.5,16){\line(1,0){1}}
%\put(19.5,18){\line(1,0){1}}
%\put(19.5,22){\line(1,0){1}}
\put(19.5,24){\line(1,0){1}}
%\put(19.5,26){\line(1,0){1}}
\put(19.5,28){\line(1,0){1}}
%\put(19.5,30){\line(1,0){1}}
\put(19.5,32){\line(1,0){1}}
%\put(19.5,34){\line(1,0){1}}
\put(19.5,36){\line(1,0){1}}
%\put(19.5,38){\line(1,0){1}}

\end{picture} }}


\def\trigGraph{{
\ifx\JPicScale\undefined\def\JPicScale{1.4}\fi
\unitlength \JPicScale mm
\begin{picture}(45,30)(0,0)
\linethickness{0.3mm}
\put(5,0){\line(0,1){30}}
\linethickness{0.3mm}
\put(5,0){\line(1,0){40}}
\linethickness{0.3mm}
\put(5,30){\line(1,0){40}}
\linethickness{0.3mm}
\put(45,0){\line(0,1){30}}
\linethickness{0.3mm}
\multiput(15,0)(0,1.94){16}{\line(0,1){0.97}}
\linethickness{0.3mm}
\multiput(25,0)(0,1.94){16}{\line(0,1){0.97}}
\linethickness{0.3mm}
\multiput(35,0)(0,1.94){16}{\line(0,1){0.97}}
\linethickness{0.3mm}
\put(5,15){\line(1,0){40}}
\end{picture}\\
}}

\def\polar{{
\ifx\JPicScale\undefined\def\JPicScale{1.0}\fi
\unitlength \JPicScale mm
\begin{picture}(40,40)(0,0)
\linethickness{0.15mm}
\put(40,19.75){\line(0,1){0.5}}
\multiput(39.99,19.25)(0.01,0.5){1}{\line(0,1){0.5}}
\multiput(39.96,18.75)(0.02,0.5){1}{\line(0,1){0.5}}
\multiput(39.92,18.26)(0.04,0.5){1}{\line(0,1){0.5}}
\multiput(39.87,17.76)(0.05,0.5){1}{\line(0,1){0.5}}
\multiput(39.81,17.27)(0.06,0.49){1}{\line(0,1){0.49}}
\multiput(39.74,16.77)(0.07,0.49){1}{\line(0,1){0.49}}
\multiput(39.65,16.28)(0.09,0.49){1}{\line(0,1){0.49}}
\multiput(39.55,15.79)(0.1,0.49){1}{\line(0,1){0.49}}
\multiput(39.44,15.31)(0.11,0.49){1}{\line(0,1){0.49}}
\multiput(39.32,14.82)(0.12,0.48){1}{\line(0,1){0.48}}
\multiput(39.18,14.34)(0.14,0.48){1}{\line(0,1){0.48}}
\multiput(39.04,13.87)(0.15,0.48){1}{\line(0,1){0.48}}
\multiput(38.88,13.39)(0.16,0.47){1}{\line(0,1){0.47}}
\multiput(38.71,12.93)(0.17,0.47){1}{\line(0,1){0.47}}
\multiput(38.52,12.46)(0.09,0.23){2}{\line(0,1){0.23}}
\multiput(38.33,12)(0.1,0.23){2}{\line(0,1){0.23}}
\multiput(38.13,11.55)(0.1,0.23){2}{\line(0,1){0.23}}
\multiput(37.91,11.1)(0.11,0.22){2}{\line(0,1){0.22}}
\multiput(37.68,10.65)(0.11,0.22){2}{\line(0,1){0.22}}
\multiput(37.44,10.22)(0.12,0.22){2}{\line(0,1){0.22}}
\multiput(37.19,9.78)(0.12,0.22){2}{\line(0,1){0.22}}
\multiput(36.93,9.36)(0.13,0.21){2}{\line(0,1){0.21}}
\multiput(36.66,8.94)(0.14,0.21){2}{\line(0,1){0.21}}
\multiput(36.38,8.53)(0.14,0.21){2}{\line(0,1){0.21}}
\multiput(36.09,8.12)(0.15,0.2){2}{\line(0,1){0.2}}
\multiput(35.79,7.73)(0.1,0.13){3}{\line(0,1){0.13}}
\multiput(35.48,7.34)(0.1,0.13){3}{\line(0,1){0.13}}
\multiput(35.16,6.95)(0.11,0.13){3}{\line(0,1){0.13}}
\multiput(34.83,6.58)(0.11,0.12){3}{\line(0,1){0.12}}
\multiput(34.49,6.21)(0.11,0.12){3}{\line(0,1){0.12}}
\multiput(34.14,5.86)(0.12,0.12){3}{\line(0,1){0.12}}
\multiput(33.79,5.51)(0.12,0.12){3}{\line(1,0){0.12}}
\multiput(33.42,5.17)(0.12,0.11){3}{\line(1,0){0.12}}
\multiput(33.05,4.84)(0.12,0.11){3}{\line(1,0){0.12}}
\multiput(32.66,4.52)(0.13,0.11){3}{\line(1,0){0.13}}
\multiput(32.27,4.21)(0.13,0.1){3}{\line(1,0){0.13}}
\multiput(31.88,3.91)(0.13,0.1){3}{\line(1,0){0.13}}
\multiput(31.47,3.62)(0.2,0.15){2}{\line(1,0){0.2}}
\multiput(31.06,3.34)(0.21,0.14){2}{\line(1,0){0.21}}
\multiput(30.64,3.07)(0.21,0.14){2}{\line(1,0){0.21}}
\multiput(30.22,2.81)(0.21,0.13){2}{\line(1,0){0.21}}
\multiput(29.78,2.56)(0.22,0.12){2}{\line(1,0){0.22}}
\multiput(29.35,2.32)(0.22,0.12){2}{\line(1,0){0.22}}
\multiput(28.9,2.09)(0.22,0.11){2}{\line(1,0){0.22}}
\multiput(28.45,1.87)(0.22,0.11){2}{\line(1,0){0.22}}
\multiput(28,1.67)(0.23,0.1){2}{\line(1,0){0.23}}
\multiput(27.54,1.48)(0.23,0.1){2}{\line(1,0){0.23}}
\multiput(27.07,1.29)(0.23,0.09){2}{\line(1,0){0.23}}
\multiput(26.61,1.12)(0.47,0.17){1}{\line(1,0){0.47}}
\multiput(26.13,0.96)(0.47,0.16){1}{\line(1,0){0.47}}
\multiput(25.66,0.82)(0.48,0.15){1}{\line(1,0){0.48}}
\multiput(25.18,0.68)(0.48,0.14){1}{\line(1,0){0.48}}
\multiput(24.69,0.56)(0.48,0.12){1}{\line(1,0){0.48}}
\multiput(24.21,0.45)(0.49,0.11){1}{\line(1,0){0.49}}
\multiput(23.72,0.35)(0.49,0.1){1}{\line(1,0){0.49}}
\multiput(23.23,0.26)(0.49,0.09){1}{\line(1,0){0.49}}
\multiput(22.73,0.19)(0.49,0.07){1}{\line(1,0){0.49}}
\multiput(22.24,0.13)(0.49,0.06){1}{\line(1,0){0.49}}
\multiput(21.74,0.08)(0.5,0.05){1}{\line(1,0){0.5}}
\multiput(21.25,0.04)(0.5,0.04){1}{\line(1,0){0.5}}
\multiput(20.75,0.01)(0.5,0.02){1}{\line(1,0){0.5}}
\multiput(20.25,0)(0.5,0.01){1}{\line(1,0){0.5}}
\put(19.75,0){\line(1,0){0.5}}
\multiput(19.25,0.01)(0.5,-0.01){1}{\line(1,0){0.5}}
\multiput(18.75,0.04)(0.5,-0.02){1}{\line(1,0){0.5}}
\multiput(18.26,0.08)(0.5,-0.04){1}{\line(1,0){0.5}}
\multiput(17.76,0.13)(0.5,-0.05){1}{\line(1,0){0.5}}
\multiput(17.27,0.19)(0.49,-0.06){1}{\line(1,0){0.49}}
\multiput(16.77,0.26)(0.49,-0.07){1}{\line(1,0){0.49}}
\multiput(16.28,0.35)(0.49,-0.09){1}{\line(1,0){0.49}}
\multiput(15.79,0.45)(0.49,-0.1){1}{\line(1,0){0.49}}
\multiput(15.31,0.56)(0.49,-0.11){1}{\line(1,0){0.49}}
\multiput(14.82,0.68)(0.48,-0.12){1}{\line(1,0){0.48}}
\multiput(14.34,0.82)(0.48,-0.14){1}{\line(1,0){0.48}}
\multiput(13.87,0.96)(0.48,-0.15){1}{\line(1,0){0.48}}
\multiput(13.39,1.12)(0.47,-0.16){1}{\line(1,0){0.47}}
\multiput(12.93,1.29)(0.47,-0.17){1}{\line(1,0){0.47}}
\multiput(12.46,1.48)(0.23,-0.09){2}{\line(1,0){0.23}}
\multiput(12,1.67)(0.23,-0.1){2}{\line(1,0){0.23}}
\multiput(11.55,1.87)(0.23,-0.1){2}{\line(1,0){0.23}}
\multiput(11.1,2.09)(0.22,-0.11){2}{\line(1,0){0.22}}
\multiput(10.65,2.32)(0.22,-0.11){2}{\line(1,0){0.22}}
\multiput(10.22,2.56)(0.22,-0.12){2}{\line(1,0){0.22}}
\multiput(9.78,2.81)(0.22,-0.12){2}{\line(1,0){0.22}}
\multiput(9.36,3.07)(0.21,-0.13){2}{\line(1,0){0.21}}
\multiput(8.94,3.34)(0.21,-0.14){2}{\line(1,0){0.21}}
\multiput(8.53,3.62)(0.21,-0.14){2}{\line(1,0){0.21}}
\multiput(8.12,3.91)(0.2,-0.15){2}{\line(1,0){0.2}}
\multiput(7.73,4.21)(0.13,-0.1){3}{\line(1,0){0.13}}
\multiput(7.34,4.52)(0.13,-0.1){3}{\line(1,0){0.13}}
\multiput(6.95,4.84)(0.13,-0.11){3}{\line(1,0){0.13}}
\multiput(6.58,5.17)(0.12,-0.11){3}{\line(1,0){0.12}}
\multiput(6.21,5.51)(0.12,-0.11){3}{\line(1,0){0.12}}
\multiput(5.86,5.86)(0.12,-0.12){3}{\line(1,0){0.12}}
\multiput(5.51,6.21)(0.12,-0.12){3}{\line(0,-1){0.12}}
\multiput(5.17,6.58)(0.11,-0.12){3}{\line(0,-1){0.12}}
\multiput(4.84,6.95)(0.11,-0.12){3}{\line(0,-1){0.12}}
\multiput(4.52,7.34)(0.11,-0.13){3}{\line(0,-1){0.13}}
\multiput(4.21,7.73)(0.1,-0.13){3}{\line(0,-1){0.13}}
\multiput(3.91,8.12)(0.1,-0.13){3}{\line(0,-1){0.13}}
\multiput(3.62,8.53)(0.15,-0.2){2}{\line(0,-1){0.2}}
\multiput(3.34,8.94)(0.14,-0.21){2}{\line(0,-1){0.21}}
\multiput(3.07,9.36)(0.14,-0.21){2}{\line(0,-1){0.21}}
\multiput(2.81,9.78)(0.13,-0.21){2}{\line(0,-1){0.21}}
\multiput(2.56,10.22)(0.12,-0.22){2}{\line(0,-1){0.22}}
\multiput(2.32,10.65)(0.12,-0.22){2}{\line(0,-1){0.22}}
\multiput(2.09,11.1)(0.11,-0.22){2}{\line(0,-1){0.22}}
\multiput(1.87,11.55)(0.11,-0.22){2}{\line(0,-1){0.22}}
\multiput(1.67,12)(0.1,-0.23){2}{\line(0,-1){0.23}}
\multiput(1.48,12.46)(0.1,-0.23){2}{\line(0,-1){0.23}}
\multiput(1.29,12.93)(0.09,-0.23){2}{\line(0,-1){0.23}}
\multiput(1.12,13.39)(0.17,-0.47){1}{\line(0,-1){0.47}}
\multiput(0.96,13.87)(0.16,-0.47){1}{\line(0,-1){0.47}}
\multiput(0.82,14.34)(0.15,-0.48){1}{\line(0,-1){0.48}}
\multiput(0.68,14.82)(0.14,-0.48){1}{\line(0,-1){0.48}}
\multiput(0.56,15.31)(0.12,-0.48){1}{\line(0,-1){0.48}}
\multiput(0.45,15.79)(0.11,-0.49){1}{\line(0,-1){0.49}}
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\multiput(28,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(30,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(32,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(34,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(36,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(38,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(40,0)(0,2.00){20}{\line(0,1){0.1}}

\linethickness{0.15mm}
\multiput(0,0)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,2)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,4)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,6)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,8)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,10)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,12)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,14)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,16)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,18)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,22)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,24)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,26)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,28)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,30)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,32)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,34)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,36)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,38)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,40)(2.00,0){20}{\line(1,0){0.1}}

%tick marks x axis 
\linethickness{0.2mm}
\put(0,19.5){\line(0,1){1}}
\put(2,19.5){\line(0,1){1}}
\put(4,19.5){\line(0,1){1}}
\put(6,19.5){\line(0,1){1}}
\put(8,19.5){\line(0,1){1}}
\put(10,19.5){\line(0,1){1}}
\put(12,19.5){\line(0,1){1}}
\put(14,19.5){\line(0,1){1}}
\put(16,19.5){\line(0,1){1}}
\put(18,19.5){\line(0,1){1}}
\put(22,19.5){\line(0,1){1}}
\put(24,19.5){\line(0,1){1}}
\put(26,19.5){\line(0,1){1}}
\put(28,19.5){\line(0,1){1}}
\put(30,19.5){\line(0,1){1}}
\put(32,19.5){\line(0,1){1}}
\put(34,19.5){\line(0,1){1}}
\put(36,19.5){\line(0,1){1}}
\put(38,19.5){\line(0,1){1}}


%tick marks y axis
\linethickness{0.2mm}
\put(19.5,0){\line(1,0){1}}
\put(19.5,2){\line(1,0){1}}
\put(19.5,4){\line(1,0){1}}
\put(19.5,6){\line(1,0){1}}
\put(19.5,8){\line(1,0){1}}
\put(19.5,10){\line(1,0){1}}
\put(19.5,12){\line(1,0){1}}
\put(19.5,14){\line(1,0){1}}
\put(19.5,16){\line(1,0){1}}
\put(19.5,18){\line(1,0){1}}
\put(19.5,22){\line(1,0){1}}
\put(19.5,24){\line(1,0){1}}
\put(19.5,26){\line(1,0){1}}
\put(19.5,28){\line(1,0){1}}
\put(19.5,30){\line(1,0){1}}
\put(19.5,32){\line(1,0){1}}
\put(19.5,34){\line(1,0){1}}
\put(19.5,36){\line(1,0){1}}
\put(19.5,38){\line(1,0){1}}
\end{picture} }}

\def\gridNoTicks{{%
\ifx\JPicScale\undefined\def\JPicScale{1.7}\fi
\unitlength \JPicScale mm\begin{picture}(40,40)(0,0)
\linethickness{0.15mm}
\multiput(0,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(2,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(4,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(6,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(8,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(10,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(12,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(14,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(16,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(18,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(22,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(24,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(26,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(28,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(30,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(32,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(34,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(36,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(38,0)(0,2.00){20}{\line(0,1){0.1}}
\multiput(40,0)(0,2.00){20}{\line(0,1){0.1}}

\linethickness{0.15mm}
\multiput(0,0)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,2)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,4)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,6)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,8)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,10)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,12)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,14)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,16)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,18)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,22)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,24)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,26)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,28)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,30)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,32)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,34)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,36)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,38)(2.00,0){20}{\line(1,0){0.1}}
\multiput(0,40)(2.00,0){20}{\line(1,0){0.1}}
\end{picture}\\ }}
