using namespace std;

#include <set>
#include <map>
#include <list>
#include <deque>
#include <stack>
#include <queue>
#include <cmath>
#include <cstdio>
#include <vector>
#include <string>
#include <bitset>
#include <utility>
#include <algorithm>

#define pb push_back
#define sz size
#define f first
#define s second
#define II inline
#define ll long long
#define db double
#define FOR(i,a,b) for(int i=a;i<=b;++i)
#define all(v) v.begin() , v.end()
#define CC(v) memset((v),0,sizeof((v)))
#define CP(v,w) memcpy((v),(w),sizeof((w)))
#define mp make_pair

#define IN  "puteri.in"
#define OUT "puteri.out"
#define N_MAX 1<<17
#define MOD 65535

int mod,N,P[1<<8];
int K,NR[1<<8],V[N_MAX];
vector<bool> viz(1<<8);
vector<bool> bo(1<<8);
char buffer[1<<20];

II void read(int &aux)
{
	aux = 0;
	for(;buffer[K] < '0' || buffer[K] > '9';++K);
	for(;buffer[K] >= '0' && buffer[K] <= '9';++K)
		aux = aux * 10 + buffer[K] - '0';
}

II void ciur()
{
	for(int i=4;i<=(1<<7);i+=2)
		viz[i] = true;
	P[++P[0]] = 2;
	
	for(int i=3;i<=(1<<7);i+=2)
	{
		if(viz[i])
			continue;
		P[++P[0]] = i;
		for(int j=i+i;j<=(1<<7);j+=i)
			viz[j] = true;
	}	
}

II void scan()
{
	freopen(IN,"r",stdin);
	freopen(OUT,"w",stdout);
	fread(buffer,1,1<<20,stdin);
	fclose(stdin);
	
	read(N);
	int a,b,c;
	FOR(i,1,N)
	{
		read(a),read(b),read(c);
		V[i] = a * 10000 + b * 100 + c;
	}	
}

II void make(int &a,int &b,int &c,int x)
{
	c = x % 100;
	b = (x / 100) % 100;
	a = (x / 10000);
	
	a = a % mod;
	b = b % mod;
	c = c % mod;
}

II void make_2(int &a,int &b,int &c,int x)
{
	c = x % 100;
	b = (x / 100) % 100;
	a = (x / 10000);
	
	a = a % mod;
	b = b % mod;
	c = c % mod;
	if(a)
		a = mod - a;
	if(b)
		b = mod - b;
	if(c)
		c = mod - c;
}

II bool divide(int x)
{
	int nr(0),aux = x;
	for(int i=2;i*i<=x;++i)
	{
		if(aux % i)
			continue;
		++nr;
		aux /= i;
		if(!(aux % i) || !bo[i])
			return false;	
	}	
	if(aux>1)
		++nr;
	NR[x] = nr;
	return true;
}

II void solve()
{
	int a,b,c;
	short int C[66][66][66];
	ll A[1<<8];
	
	FOR(pi,2,128)
	{
		mod = pi;
		if(!viz[mod])
			NR[mod] = 1;
		if(viz[mod] && !divide(mod) )
			continue;
		for(int i=N-1;i>=1;--i)
		{
			make(a,b,c,V[i+1]);
			if(V[i+1])
				++C[a][b][c];
			
			make_2(a,b,c,V[i]);
			if(a<=64 && b<=64 && c<=64)
				A[mod] += (ll)C[a][b][c]; 
		}
		if(A[mod])
			bo[mod] = true;
		CC(C);
	}
	
	ll rez(0);	
	FOR(i,2,128)  
		if(NR[i]&1)  
        	rez += A[i];  
        else  
		    rez -= A[i];  
    printf("%lld\n",rez);
}

int main()
{
	ciur();
	scan();
	solve();
//	printf("%d\n",clock() );

	return 0;
}