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标题: equation.exe控制台解方程(组)工具 [打印本页]

作者: happy886rr    时间: 2016-12-5 21:30     标题: equation.exe控制台解方程(组)工具

EQUATION.EXE

摘要:
=============================================================================
这是一个专注解方程和方程组的简单工具,帮助那些想快速计算出结果的童鞋们。求解
结果精确到小数点后12位,且支持复根。
=============================================================================

用法:
-----------------------------------------------------------------------------
equation [/O {parameters}]|[/M]|[/R {parameters}]
-----------------------------------------------------------------------------
  /H  显示帮助信息
  /O  求解一元方程
  /M  求解多元方程组
  /R  求解单位复元根
-----------------------------------------------------------------------------

示例:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
equation /O  3 0 5 -6 -9        //求解一元四次方程3x^4+0x^3+5x^2-6x-9=0
The solution of the equation 3x^4+0x^3+5x^2-6x-9=0 is:
┌────────────────────────┐
  Imag   root: -0.252438186547+1.696390660707i
               -0.252438186547-1.696390660707i
  Real   root:  1.293411063722
               -0.788534690627
└────────────────────────┘

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
equation /R  5                  //求解5次复元根 x^5-1=0
┌────────────────────────┐
        x[ 1]= 0.309016994375+0.951056516295i
        x[ 2]=-0.809016994375+0.587785252292i
        x[ 3]=-0.809016994375-0.587785252292i
        x[ 4]= 0.309016994375-0.951056516295i
        x[ 5]= 1.000000000000-0.000000000000i
└────────────────────────┘

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
equation /M                     //进入方程组模式

        [Multivariable Equations]   ---Quit using "q"
        {2                      //此处输入方程组个数
        Equation coefficients:
        3 2 5                   //第一个方程式的系数
        6 9 1                   //第二个方程式的系数
        Solution of equations:
        ┌───────────────┐
          x[0]= 2.866666793823
          x[1]=-1.800000071526
        └───────────────┘
        {{q                     //输入q退出该模式

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


英译:
-----------------------------------------------------------------------------
CONSOLE SOLVING EQUATION TOOLS, COPYRIGHT@2016~2018 BY HAPPY, VERSION 1.0
-----------------------------------------------------------------------------
equation [/O {parameters}]|[/M]|[/R {parameters}]
-----------------------------------------------------------------------------
  /H  Displays help information
  /O  Solves the univariate equation
  /M  Solving Systems of multivariable Equations
  /R  Solve the unit root
-----------------------------------------------------------------------------
12/03/2016


核心代码:
  1. /*
  2.     CONSOLE SOLVING EQUATION TOOLS, COPYRIGHT@2016~2018 BY HAPPY
  3.     EQUATION.EXE
  4.     VERSION 1.0
  5. */
  6. #include <stdio.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <math.h>
  10. //定义帮助说明//////////////////////////////////////////////////////
  11. #define HELPINFORMATION "\
  12. SOLVING EQUATION TOOLS, COPYRIGHT@2016~2018 BY HAPPY, VERSION 1.0\n\
  13. -----------------------------------------------------------------\n\
  14. equation [/O {parameters}]|[/M]|[/R {parameters}]\n\
  15. -----------------------------------------------------------------\n\
  16.   /H  Displays help information\n\
  17.   /O  Solves the univariate equation\n\
  18.   /M  Solving Systems of multivariable Equations\n\
  19.   /R  Solve the unit root\n\
  20. -----------------------------------------------------------------\n\
  21. 12/03/2016\n"
  22. ////////////////////////////////////////////////////////////////////
  23. /***************功能函数群***************/
  24. void equation_set(int n)
  25. {  
  26.     int i, j, m, r, k=0, t, mark;
  27.     float a[11][12];
  28.     printf("Equation coefficients:\n");
  29.     r=n;  
  30.     for(j=0; j<n; j++){   
  31.         for(i=0; i<r+1; i++){   
  32.             scanf("%f", &a[j][i]);
  33.         }
  34.         if(a[j][0]!=0){mark=j;}
  35.     }
  36.     //系数修正
  37.     for(j=0; j<n; j++){
  38.         if(a[j][0]+a[mark][0] != 0){   
  39.             for(i=0; i<r+1; i++){   
  40.                 a[j][i] += a[mark][i];
  41.             }
  42.         }
  43.     }
  44.     if(r==n)
  45.     {   
  46.         printf("Solution of equations:\n");
  47.         for(t=0; t<n-1; t++)
  48.             for(m=0; m<n; m++)
  49.                 for(j=0; j<n; j++)
  50.                     if(j!=m)     
  51.                     {  
  52.                         float b= a[j][m]/a[m][m];
  53.                         for(i=0; i<n+1; i++)
  54.                             a[j][i] -= a[m][i]*b;                     
  55.                     }
  56.         for(j=0; j<n; j++)     
  57.         {   
  58.                 a[j][n] /=a[j][j];   
  59.                 a[j][j] /=a[j][j];
  60.         }
  61.     }
  62.     printf("┌───────────────┐\n");
  63.     for(j=0; j<r; j++){   
  64.         printf("   x[%d]=%15.12f\n", j, a[j][n]);
  65.     }
  66.     printf("└───────────────┘\n");
  67. }
  68. void twice(double a, double b, double c)
  69. {
  70.     double x1,x2,den=2*a,delt=b*b-4*a*c;
  71.     if(a==0){
  72.         if(b==0){
  73.             printf("  Not a real equation");
  74.         }
  75.         else{
  76.             printf("  Reduced to once equation\n  Real   root: x=%.12lf",-c/b);
  77.         }
  78.     }
  79.     else{   
  80.         if(delt>0){
  81.             x1=-b/den+sqrt(delt)/den;
  82.             x2=-b/den-sqrt(delt)/den;
  83.             printf("  Real   root: %15.12lf\n               %15.12lf",x1,x2);
  84.         }
  85.         else if(delt==0){
  86.             printf("  Double root: %15.12lf",-b/den);
  87.         }
  88.         else if(delt<0){
  89.             x1=sqrt(-delt)/den;
  90.             printf("  Imag   root: %15.12lf+%.12lfi\n               %15.12lf-%.12lfi",-b/den,x1,-b/den,x1);
  91.         }
  92.     }
  93. }
  94. double thice(double a, double b, double c, double d, int gk)
  95. {
  96.     double A=b*b-3*a*c,B=b*c-9*a*d,C=c*c-3*b*d,delta=B*B-4*A*C;
  97.     if(A==0 && B==0){
  98.         if(gk!=1){printf("  Triple real: %15.12lf",-b/(3*a));}
  99.         return -b/(3*a);
  100.     }
  101.     else if(delta>0){
  102.         double Y1=A*b+3*a*(-B+sqrt(delta))/2.0,Y2=A*b+3*a*(-B-sqrt(delta))/2.0;
  103.         Y1=(Y1>0)? pow(Y1,1.0/3.0) :-pow(-Y1,1.0/3.0);
  104.         Y2=(Y2>0)? pow(Y2,1.0/3.0) :-pow(-Y2,1.0/3.0);
  105.         double x1=(-b-Y1-Y2)/(3.0*a);
  106.         double prr=(-2*b+Y1+Y2)/(6.0*a),pri=(Y1-Y2)*sqrt(3)/(6.0*a);
  107.         if(gk!=1){printf("  First  real: %15.12lf\n  Imag   root: %15.12lf+%.12lfi\n               %15.12lf-%.12lfi",x1,prr,pri,prr,pri);}
  108.         return x1;
  109.     }
  110.     else if(delta==0){
  111.         if(gk!=1){printf("  Double real: %15.12lf\n               Other  real: %15.12lf\n",-B/(2.0*A),-b/a+B/A);}
  112.         if(-B/(2.0*A) > -b/a+B/A){
  113.             return -B/(2.0*A);
  114.         }else{
  115.             return -b/a+B/A;
  116.         }
  117.     }
  118.     else if(delta<0){
  119.         double r=acos((2*A*b-3*a*B)/(2*A*sqrt(A)));   
  120.         double x1=(-b-2.0*sqrt(A)*cos(r/3.0))/(3.0*a);
  121.         double x2=(-b-2*sqrt(A)*cos((r+2*M_PI)/3.0))/(3.0*a);
  122.         double x3=(-b-2*sqrt(A)*cos((r+4*M_PI)/3.0))/(3.0*a);
  123.         if(gk!=1){printf("  Triple real: %15.12lf\n               %15.12lf\n               %15.12lf",x1,x2,x3);}
  124.         double tempv;
  125.         if(x1 > x2){
  126.             tempv=x1;
  127.         }else{
  128.             tempv=x2;
  129.         }
  130.         if(tempv > x3){
  131.             return tempv;
  132.         }else{
  133.             return x3;
  134.         }
  135.     }
  136. }
  137. void foice(double a, double b, double c, double d, double e)
  138. {
  139.     double y,f[4],M,N,P;
  140.     int i;
  141.     b/=a;c/=a;d/=a;e/=a;a=1;
  142.     f[0]=8;
  143.     f[1]=-4.0*c;
  144.     f[2]=-(8.0*e-2.0*b*d);
  145.     f[3]=-e*(b*b-4.0*c)-d*d;
  146.     y=thice(f[0],f[1],f[2],f[3],1);
  147.     M=sqrt(8.0*y+b*b-4.0*c);
  148.     N=b*y-d;
  149.     if(M==0){
  150.         P=sqrt(y*y-e);
  151.         twice(2.0,b,2.0*(y+P));
  152.         printf("\n");
  153.         twice(2.0,b,2.0*(y-P));
  154.     }else{
  155.         twice(2.0,b+M,2.0*(y+N/M));
  156.         printf("\n");
  157.         twice(2.0,b-M,2.0*(y-N/M));
  158.     }
  159. }
  160. void fifth(double a, double b, double c, double d, double e, double f)
  161. {
  162.      double r,x,F,F1;
  163.      b/=a;c/=a;d/=a;e/=a;f/=a;
  164.      a=-1.0;
  165.     do
  166.     {
  167.            x=a;
  168.            F=x*x*x*x*x+b*x*x*x*x+c*x*x*x+d*x*x+e*x+f;
  169.            F1=5*x*x*x*x+4*b*x*x*x+3*c*x*x+2*d*x+e;
  170.            a=x-F/F1;   
  171.     }
  172.     while(fabs(x-a)>=1e-10);
  173.     double e1=-f/x,d1=(e1-e)/x,c1=(d1-d)/x,b1=(c1-c)/x;
  174.     foice(1.0,b1,c1,d1,e1);
  175.     printf ("\n  Iterative  : %15.12lf",x);
  176. }
  177. /***************业务函数群***************/
  178. //字符串转等式
  179. char* atop(char *s)
  180. {
  181.     if(atof(s)>=0){
  182.         char *r=malloc(strlen(s)+strlen("+")+1);
  183.         strcpy(r,"+");strcat(r,s);  
  184.         return r;
  185.     }
  186.     return s;
  187. }
  188. //解多元方程组
  189. void Multivariable_Equations()
  190. {
  191.     char str[8];
  192.     puts("[Multivariable Equations]   ---Quit using \"q\"");
  193.     while(printf("{"),fgets(str,7,stdin)!=NULL){
  194.         char *i=strchr(str,'\n');
  195.         if(i!=NULL){*i='\0';}
  196.         if (i!=str){
  197.             if(!strcmp(str,"q")){break;}
  198.             equation_set(atoi(str));
  199.         }
  200.     }
  201. }
  202. //解一元高次方程
  203. void Univariate_Equation(int argc, char** argv)
  204. {
  205.     if(argc==4){
  206.         printf("The solution of the equation %sx%s=0 is: \n",argv[2],atop(argv[3]));
  207.         printf("┌────────────────────────┐\n");
  208.         if(atof(argv[2])==0){printf("  Not a real equation");}else{printf("  %15.12lf",-atof(argv[3])/atof(argv[2]));}
  209.         printf("\n└────────────────────────┘");
  210.     }
  211.     else if(argc==5){
  212.         printf("The solution of the equation %sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]));
  213.         printf("┌────────────────────────┐\n");
  214.         twice(atof(argv[2]),atof(argv[3]),atof(argv[4]));
  215.         printf("\n└────────────────────────┘");
  216.     }
  217.     else if(argc==6){
  218.         printf("The solution of the equation %sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]));
  219.         printf("┌────────────────────────┐\n");
  220.         if(atof(argv[2])==0){
  221.             printf("  Reduced to a quadratic equation\n");
  222.             twice(atof(argv[3]),atof(argv[4]),atof(argv[5]));
  223.         }
  224.         else{
  225.             thice(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),0);
  226.         }
  227.         printf("\n└────────────────────────┘");
  228.     }
  229.     else if(argc==7){
  230.         printf("The solution of the equation %sx^4%sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]),atop(argv[6]));
  231.         printf("┌────────────────────────┐\n");
  232.         if(atof(argv[2])==0){
  233.             printf("  Reduced to cubic equation\n");
  234.             if(atof(argv[3])==0){
  235.                 printf("  Reduced to a quadratic equation\n");
  236.                 twice(atof(argv[4]),atof(argv[5]),atof(argv[6]));
  237.             }else{
  238.                 thice(atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),0);
  239.             }
  240.         }
  241.         else{
  242.             foice(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]));
  243.         }
  244.         printf("\n└────────────────────────┘");
  245.     }
  246.     else if(argc==8){
  247.         printf("The solution of the equation %sx^5%sx^4%sx^3%sx^2%sx%s=0 is: \n",argv[2],atop(argv[3]),atop(argv[4]),atop(argv[5]),atop(argv[6]),atop(argv[7]));
  248.         printf("┌────────────────────────┐\n");
  249.         if(atof(argv[2])==0){
  250.             printf("  Reduced to foice equation\n");
  251.             if(atof(argv[3])==0){
  252.                 printf("  Reduced to cubic equation\n");
  253.                 if(atof(argv[4])==0){
  254.                     printf("  Reduced to a quadratic equation\n");
  255.                     twice(atof(argv[5]),atof(argv[6]),atof(argv[7]));
  256.                 }else{
  257.                     thice(atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]),0);
  258.                 }
  259.                
  260.             }else{
  261.                 foice(atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]));
  262.             }
  263.         }else{
  264.             fifth(atof(argv[2]),atof(argv[3]),atof(argv[4]),atof(argv[5]),atof(argv[6]),atof(argv[7]));
  265.         }
  266.         printf("\n└────────────────────────┘");
  267.     }
  268. }
  269. //单位元根
  270. void Unit_Root(int argc, char** argv)
  271. {
  272.     if(argc!=3){
  273.         printf("Missing parameters\n");
  274. exit(1);
  275. }
  276.     int i, n=atoi(argv[2]);
  277.     printf("┌──────────────────────┐\n");
  278.     for(i=1; i<n; i++){
  279.         if(i==n){printf("     r[%2d]=%15.12lf%.12lfi",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));break;}
  280.         if(sin(2*i*M_PI/n)<0){
  281.             printf("     r[%2d]=%15.12lf%.12lfi\n",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));
  282.         }
  283.         else{
  284.             printf("     r[%2d]=%15.12lf+%.12lfi\n",i,cos(2*i*M_PI/n),sin(2*i*M_PI/n));
  285.         }   
  286.     }
  287.     printf("     r[%2d]= 1.000000000000", n);
  288.     printf("\n└──────────────────────┘");
  289. }
  290. /*************MAIN主函数入口*************/
  291. int main(int argc, char** argv)
  292. {
  293.     if( (argc >1) && (argv[1][0]=='/') )
  294.     {
  295.         switch(argv[1][1])
  296.         {
  297.             case 'H':
  298.             case 'h':
  299.                 fputs(HELPINFORMATION,stdout);
  300.                 exit(0);
  301.             case 'M':
  302.             case 'm':
  303.                 Multivariable_Equations();
  304.                 break;
  305.             case 'O':
  306.             case 'o':
  307.                 Univariate_Equation(argc, argv);
  308.                 break;
  309.             case 'R':
  310.             case 'r':
  311.                 Unit_Root(argc, argv);
  312.                 break;
  313.             default:
  314.                 fputs(HELPINFORMATION,stdout);
  315.                 exit(1);
  316.         }
  317.         return 0;
  318.     }
  319.     fputs(HELPINFORMATION,stdout);
  320.     exit(1);
  321. }
复制代码
文件下载: base64加权
  1. @echo off
  2. setlocal enabledelayedexpansion
  3. ::*********BASE64 加权解码器*********
  4. set $=set [#]&CALL :BASE64_PRESS&set [$]=A&((for %%Z in ([,],{,},_,$,#,-,@) do (set [$]=![$]!![$]!&for %%S in (![$]!) do (for /l %%i in (1,1,15) do (!$!%%i=![#]%%i:%%Z=%%S!))))&for /l %%i in (1,1,15) do (set/p=![#]%%i:.=!<NUL))>equation.BSEP&certutil -decode equation.BSEP equation.zip&pause&exit /b
  5. ::***********************************
  6. :BASE64_PRESS
  7. !$!1=UEsDBAo][CechEk}E]c3JjL1BLAwQU]CADxm4RJKV3qpMQK[A5Kw[Dg[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  11. !$!5=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
  12. !$!6=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[EYEQwfnIz+g70iUuQTJ2SqVUyNcl1OGhskoytkrFThAkRu8Uu73kIJ3RzVwfcZwB6q7yaILYCEJ9wwL6LANzyPQTgBsBfgYrkS3he1Q8
  13. !$!7=dxZVjmg0TLkauyzEwOO3dQqdkZGFI6BG7iXu1wnFo9widYk9f+TAMQTQAcl+mVujqP4uYx/u7xHahW+zpPyVGlhLYcH8XuhtHAvHyyNY1oNJpbC7dukQS6N8KboYYWUYZ9tXqwZ2lq4g7NfILN5GAFGIRLJkwMvts2vqjqPdaU4fYFVj/hKvuGRvG3kkgETvEMTrdJJD6MvUQMNSiNtGDlazb/pcInNtTcBePg3DxuBJ1wofgYYiwvkwZxkwkzCDO+2KbUEtjm267i1B+J4LEslEgRoIQoJFOfTCAnt8dxP5OJSw2KbIKupQvrk9lbprkgzPI7KKMXuRCGdTZ3qsDezYEKQk+EMo8IdCvECO3EKfpSUSS+QMdzL2oiBaUN0JLOA2lA6wrh07/eTGyhvoZjalDguPCOfF4/zldw6/UGPoQwBpyTxC7SYijrnFiFwY3TEwdTgzoPH4j0TkwESWN1P8Nf1ahL6VBmhCeeQvVNw7jRHQTpQQPKDuG8UYmRspvFY/v7u+BODqt235UjU59E+79Xf2XwFz5SZRj6sTIp6vxPYLyLtz7YveQmPBIxs6+O1uxDQRGIOjL9PSZ9QSi7YtFSF+th3T9XJ4iXB4P4eJGLpHbEDfA69INyMtNeLlDeLlJ18/rc5JrLmLcIYtGJI5sJVNNmYvdxBZ028s3ELetoAhkGvq7cc70/ee4BJI8jG6SR4wezCrKMkDSZ29QcoCHrGMaJLs3R0oCkpxCVb5zAteB4C3BbZI/3EAymT0tMsm64WqhBpQvwuNDoaDZDQnABTcDgTjg/S4+v7Yn0IQjSuIKXcMYeVTocWYJhTCG2VArtKP6/sgcBiNYaAljihlS8xbcox++nhrjwB6wEGIRv/8SxsUAcjkS0G3TFEkMhJkk+DH6271PfU7VGRzAfBZIdtvkVYT7Nkh26y/7fEq+BbXfV9Iq2k/0kJpLUZuZgK+kPwcO+NVqEnsw1XoHPqOJVoxsAxzv5M+pzvA
  14. !$!8=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
  15. !$!9=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
  16. !$!10=lfZXHKulLHqciH41V0tfAOJWwIpbkRalZwAFgcbdfqd5xqtScWLqYmzvHqR3xRCl5nIidLTkGxv3qCeN+9XrH/eohVfDwvWMEFMz6jCpzOCbwwD8UM+GB/2IMPvC9745R5O8FkZ+biFxGkZcqnM1B5PUTke9FZNMZ75jC+ptB7LSJ2NMIdqd3r8I7CrEp9qSJ2KenIHaPd42CfXJKAFuYMgH7lSlE7WIF+T+CyL+YiLyNsN7l/S8Fuy6IXTsR+xGCvcN7XsHOCWJnTcSeS7CbvC8r2AlB7JkTscejidq/UZAvRgeQL0RPQH6XIvddpMjdQeRjE5H3IXIz7hW8zykELwYJXphIYCUEuM3w3qMQlAYJzBMJlhAC3KF4/zqizH+QIG0iwTRCgJsb766RwOq+NlpZ3VuU1a2OVlZ3lbK6z0WRhZSqnJNJ/o9Ssgg9x5GVUhVYyIjl3Y+Ll27z2qJIbpSatUo2+HEUzZDNjI+u1e9G0QzWPKqs1doosiOSmoeVtVoWhWtVG0ggTEDuaGCFIq73YFDuAr9cVpF7u19uvCL3a1QumqZXTIsImMYGRMQHTEMsspJDfp/C7brBaYyx12ojdI4q3DFla18nx3RQ/Am6d4uH9M2/LTugt/BTnestgD50UpNgP6qRTPLgcklwxd2YQwf6YrUP0TfB+JZCkOdoyVlRj1sP0PnbuIt9NEGTobzdvx84yzbCt3Yj8G5w4mY95sZVV+d2cjLZxJA35OLH5L0Nfag9Q6YSBEShPBwPSEHpIGkDSppCJNW8oNiPwQWgBgQNT8bfN7V7oG0/alj7mMnbDyMuzV3ZV1cle3KYYc9PpuwUu04gy+bJ4SJcE0Q8MZn492OE3k7b6Hr5s0kgehOT79aT9yX2oQX2M8O8DU5qMXztZWctnOYuyI8Bkizi2cWnelLrvE9TtyCZWwQs9KCo8048XB3+k4oEhDKj4BL72yzuuOT6SUFprkl4RONuY3RvGlR2ebl99I7
  17. !$!11=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
  18. !$!12=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
  19. !$!13=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
  20. !$!14=hoFWtLi8sK6uEdbhVXQ6Z1AzYT6qrKjczT6mrqi0VHPCsV1fZuCJYtMzT2AK5z6qtRYUVJUyj2mrZUFFYxjDPQ6uC2aG2bgT1mB+orVx1USG0mkirFGbix9gqM1co/9fxirLCmPOgceX8eUnFZWU4X3FV/7+l3LqpqJrza/PPXf8DUEsDBBQ]IAPyZhElKrZZVkAM[CML[AK]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
  21. !$!15=vH8IgSbU/Hh34n6J6uVljR+hK9RczjnUzXbDSH2dMiB1r2COsTAXhStFyoGhbuetwbuIc5U9ieIV4pVW52/wl2KB62Dyi7doVCMK1vDk2Zl2zzJxj99AXCmAgoULuD2z8MZlmza1vub6QCgbIr+A/eH6WnzzxdQki4208u/AfKhOglEI09VjUVQbNUHSsHL+gNUs/Abqff00mWGWy/1YEqyx6kxMQBklikZvYaC0eVteD3Ex1EjznjeWZ9sFbGMsX4wPJ+OUY0OVq38AlCG5KMBSPX06eh4vxweFE36Xeofcwbbcpuujw/jD0XhgcHD4PV2OJJCPTNvvfXhg+sOzxTPqWDTfMzDhYubF8IesdLLg90HK9adreHCzm/H50/h6JwX2CsVgvJm/Zjpm1WW1nw/s3uGt4uoGs482njrsoYwkpEkvtC1BLAQIf[o][CechEk}EACQ{AE{ABzcmMvCgAg][ABABgAWRgwNCJO0gFZGDA0Ik7SAWw8/9qbTNIBUEsBAh8AF]AgA8ZuESSld6qTECg[OSs[A4AJ{[g]Ig[AHNyYy9lcXVhdGlvbi5jCgAg][ABABgAB40P+CFO0gE/aB2AIE7SAT9oHYAgTtIBUEsBAh8AF]AgA9puESRUvJEp2Gw[ADw[AwAJ{[g]Egs[GVxdWF0aW9uLmV4ZQoAI{QAYACKWZP4hTtIBwTRi/iFO0gHBNGL+IU7SAVBLAQIfABQ]IAPyZhElKrZZVkAM[CML[AKACQ{AI]LIm[ByZWFkbWUudHh0CgAg][ABABgAl/xHyR9O0gHZRzf0C07SAdlHN/QLTtIBUEsFBg]AE[QAcAE[Goq][==
  22. goto :EOF
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