#include <stdio.h>
#include <string.h>
#define Nmax 100002
#define Vmax 64+64+1
#define Rmax 65

int a[Nmax],b[Nmax],c[Nmax];
int p[Vmax],prim[Vmax],Nr[Vmax];
int r[Rmax][Rmax][Rmax],uzz[Rmax][Rmax][Rmax];
int N,z;

void ciur(){
	int i,j;
	for(i=2;i<Vmax;++i)
		if( p[i]==0 ){
			prim[++z]=i;
			for(j=i; j<Vmax; j+=i)
				if( p[j]!=-1)
					++p[j];
			for(j=i*i; j<Vmax; j+=i*i)
				p[j]=-1;
		}
}

int main(){
	int i,j,aa,bb,cc,rez=0,aa2,bb2,cc2;
	freopen("puteri.in","r",stdin);
	freopen("puteri.out","w",stdout);
	scanf("%d",&N);
	for(i=1;i<=N;++i) scanf("%d%d%d",&a[i],&b[i],&c[i]);
	
	ciur();
	
	for(i=2;i<Vmax;++i){
		memset(r,0,sizeof(r));
		memset(uzz,0,sizeof(uzz));
		
		for(j=1;j<=N;++j)
			++r[a[j]%i][b[j]%i][c[j]%i];
		
		for(j=1;j<=N;++j)
			if( ! uzz[a[j]%i][b[j]%i][c[j]%i] ){
				aa=a[j]%i; bb=b[j]%i; cc=c[j]%i;
				aa2=(i-aa)%i; bb2=(i-bb)%i; cc2=(i-cc)%i;
				if( aa2<Rmax && bb2<Rmax && cc2<Rmax ){
					uzz[aa][bb][cc]=1;
					uzz[aa2][bb2][cc2]=1;
				
					if( aa==aa2 && bb==bb2 && cc==cc2 )
						Nr[i] += r[aa][bb][cc]*(r[aa][bb][cc]-1)/2;
					else Nr[i] += r[aa][bb][cc]*r[aa2][bb2][cc2];
				}
			}
	}
	
	for(i=2; i<Vmax; ++i)
		if(p[i] != -1 )
		if( p[i] & 1) rez += Nr[i];
		else rez -= Nr[i];

	
	printf("%d\n",rez);
	fclose(stdin); fclose(stdout);
	return 0;
}