#include <fstream>
#include <algorithm>
using namespace std;

#define int long long

struct el {
    int a, b, c;
};

ifstream in("puteri.in");
ofstream out("puteri.out");
int n;
int ans;
el v[100005];
int frec[130][130][130];
int mobius[205];
int rest[130][130];

void build_mobius() {
    mobius[1] = -1;
    for (int i = 1; i <= 128; i++) {
        if (mobius[i]) {
            mobius[i] = -mobius[i];
            for (int j = 2 * i; j <= 128; j += i) {
                mobius[j] += mobius[i];
            }
        }
    }
    for (int i = 1; i <= 128; i++) {
        mobius[i] *= -1;
    }
}

signed main() {
    in >> n;
    build_mobius();

    // precompute remainders
    for (int i = 0; i <= 128; i++)
        for (int j = 2; j <= 128; j++)
            rest[i][j] = i % j;

    for (int i = 1; i <= n; i++) {
        in >> v[i].a >> v[i].b >> v[i].c;
    }

    // inclusion-exclusion over mod i
    for (int i = 2; i <= 128; i++) {
        // build freq of residues mod i
        for (int j = 1; j <= n; j++) {
            frec[rest[v[j].a][i]][rest[v[j].b][i]][rest[v[j].c][i]]++;
        }

        long long sumprod = 0;
        long long sum_self_sq = 0;
        long long selfcomb = 0;
        int lim = min(64LL, i - 1);

        for (int a = 0; a <= lim; a++) {
            for (int b = 0; b <= lim; b++) {
                for (int c = 0; c <= lim; c++) {
                    int ra = i - a; if (ra == i) ra = 0;
                    int rb = i - b; if (rb == i) rb = 0;
                    int rc = i - c; if (rc == i) rc = 0;
                    long long f1 = frec[a][b][c];
                    long long f2 = frec[ra][rb][rc];
                    sumprod += f1 * f2;
                    if (a == ra && b == rb && c == rc) {
                        sum_self_sq += f1 * f1;
                        selfcomb += f1 * (f1 - 1) / 2;
                    }
                }
            }
        }

        long long rez = (sumprod - sum_self_sq) / 2 + selfcomb;
        ans += rez * mobius[i];

        // clear freq
        for (int j = 1; j <= n; j++) {
            frec[rest[v[j].a][i]][rest[v[j].b][i]][rest[v[j].c][i]]--;
        }
    }

    out << ans;
    return 0;
}