/* det_N.c */

#include <stdio.h>                     
#include <math.h>                     

double det2(double a11, double a12, double a21, double a22);
double det3(double a11, double a12, double a13, double a21, double a22, double a23, double a31, double a32, double a33);
double det4(double a11, double a12, double a13, double a14, double a21, double a22, double a23, double a24, double a31, double a32, double a33, double a34, double a41, double a42, double a43, double a44);

double mat[10][10];
double ans,count=0;
double a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p;
double num=3;

main(){

// timer
system("date");  

// data input 

for(a=1;a<num;a++){
mat[0][0]=a;
for(b=1;b<num;b++){
mat[0][1]=b;
for(c=1;c<num;c++){
mat[0][2]=c;
for(d=1;d<num;d++){
mat[0][3]=d;
for(e=1;e<num;e++){
mat[1][0]=e;
for(f=1;f<num;f++){
mat[1][1]=f;
for(g=1;g<num;g++){
mat[1][2]=g;
for(h=1;h<num;h++){
mat[1][3]=h;
for(i=1;i<num;i++){
mat[2][0]=i;
for(j=1;j<num;j++){
mat[2][1]=j;
for(k=1;k<num;k++){
mat[2][2]=k;
for(l=1;l<num;l++){
mat[2][3]=l;
for(m=1;m<num;m++){
mat[3][0]=m;
for(n=1;n<num;n++){
mat[3][1]=n;
for(o=1;o<num;o++){
mat[3][2]=o;
for(p=1;p<num;p++){
mat[3][3]=p;

// det calculation

//ans=det2(mat[0][0],mat[0][1],mat[1][0],mat[1][1]);
//ans=det3(mat[0][0],mat[0][1],mat[0][2],mat[1][0],mat[1][1],mat[1][2],mat[2][0],mat[2][1],mat[2][2]);

ans=det4(mat[0][0],mat[0][1],mat[0][2],mat[0][3],mat[1][0],mat[1][1],mat[1][2],mat[1][3],mat[2][0],mat[2][1],mat[2][2],mat[2][3],mat[3][0],mat[3][1],mat[3][2],mat[3][3]);

if(ans==0) count++;

}}}}}}}}}}}}}}}}

printf("count %.0lf ",count);

system("date"); // timer

exit(0);
}


double det2(double a11, double a12, double a21, double a22){

 double rdet2=a11*a22-a12*a21;
 return(rdet2);

}

double det3(double a11, double a12, double a13, double a21, double a22, double a23, double a31, double a32, double a33){

double rdet3=a11*det2(a22,a23,a32,a33)-a21*det2(a12,a13,a32,a33)+a31*det2(a12,a13,a22,a23);
 return(rdet3);

}

double det4(double a11, double a12, double a13, double a14, double a21, double a22, double a23, double a24, double a31, double a32, double a33, double a34, double a41, double a42, double a43, double a44){

double rdet4=a11*det3(a22,a23,a24,a32,a33,a34,a42,a43,a44)-a21*det3(a12,a13,a14,a32,a33,a34,a42,a43,a44)+a31*det3(a12,a13,a14,a22,a23,a24,a42,a43,a44)-a41*det3(a12,a13,a14,a22,a23,a24,a32,a33,a34);

 return(rdet4);

}