#include <stdio.h>
#include <string.h>

#define maxx 128
#define ll long long
#define maxn 100010

int n;
ll sol;
int p[maxx][maxx][maxx];
char u[maxx][maxx][maxx];
int a[maxn],b[maxn],c[maxn],d[maxx];

int count(int x)
{
    int i,j,k,rez=0;
	memset(p,0,sizeof(p));
	memset(u,0,sizeof(u));
    int d[maxn],e[maxn],f[maxn];
    
    for (i=1;i<=n;i++) 
    {
        d[i]=a[i]%x;
        e[i]=b[i]%x;
        f[i]=c[i]%x;
    }
	
	for (i=1;i<=n;++i) p[d[i]][e[i]][f[i]]++;

	for (i=1;i<=n;i++)
	if (u[d[i]][e[i]][f[i]]==0)
	{
	  if ((d[i]==(x-d[i])%x) && (e[i]==(x-e[i])%x) && (f[i]==(x-f[i])%x)) rez+=p[d[i]][e[i]][f[i]]*(p[d[i]][e[i]][f[i]]-1);
	  else rez+=p[d[i]][e[i]][f[i]]*p[(x-d[i])%x][(x-e[i])%x][(x-f[i])%x];
	  u[d[i]][e[i]][f[i]]=1;
	}

	return rez/2;
}

int diviz(int x,int &rez)
{
	int i,l=0,aux;
	l=0;rez=0;

	for (i=1;i*i<=x;++i)
      if (x%i==0) d[++l]=i;
      
    if (d[l]*d[l]==x) aux=l-1;
    else aux=l;
    
    for (i=aux;i>0;i--) d[++l]=x/d[i];
    
    for (i=2;i<=l;++i)
      if (x%d[i]==0)
      {
             rez++;
             while (x%d[i]==0) x/=d[i];
      }
      
    return (1<<rez)==l;
}

int main()
{
    freopen("puteri.in","r",stdin);
    freopen("puteri.out","w",stdout);
    
    int i,x,y;
    
    scanf("%d ",&n);
    for (i=1;i<=n;++i) scanf("%d %d %d ",&a[i],&b[i],&c[i]);
    
    for (i=2;i<=maxx;++i)
     if (diviz(i,y))
      {
            x=count(i);
//            if (x>0) printf("%d %d\n",i,x);
            if (y%2==1) sol+=x;
            else sol-=x;
      }
    
    printf("%lld\n",sol);
    
    return 0;
}