sims_sifting

#include <bits/stdc++.h>
using namespace std;

const int Maxn = 55, Maxm = 105;
int n, m;
struct perm {
    int p[Maxn];
    perm() {
        for (int i = 0; i < n; i++) p[i] = i;
    }
    perm(const perm &u) {
        for (int i = 0; i < n; i++) p[i] = u.p[i];
    }
    perm inv(void) {
        perm res;
        for (int i = 0; i < n; i++)
            res.p[p[i]] = i;
        return res;
    }
} P[Maxm], *B[Maxn][Maxn];
perm mul(perm a, perm b, int i) {
    perm res;
    for (; i < n; i++)
        res.p[i] = a.p[b.p[i]];
    return res;
}
bool vis[Maxn][Maxn];
queue <pair <int, int> > Qu;
void sifting(perm sigma) {
    for (int i = 0; i < n; i++) {
        if (B[i][sigma.p[i]] == NULL)
            return B[i][sigma.p[i]] = new perm(sigma), Qu.push(make_pair(i, sigma.p[i]));
        if (sigma.p[i] != i) sigma = mul(B[i][sigma.p[i]] -> inv(), sigma, i);
    }
}
const unsigned long long lim = 1e18;
struct output {
    unsigned long long val[4];
    output() {
        val[0] = val[1] = val[2] = 0, val[3] = 1;
    }
    output operator * (int x) {
        output res = *this;
        for (int i = 0; i <= 3; i++) {
            __int128 tmp = (__int128) res.val[i] * x;
            res.val[i - 1] += tmp / lim, res.val[i] = (long long) (tmp % lim);
        }
        for (int i = 3; i >= 0; i--)
            if (res.val[i] >= lim) res.val[i] -= lim, res.val[i - 1]++;
        return res;
    }
    void print(void) {
        bool flag = false;
        for (int i = 0; i <= 3; i++) {
            if (flag) printf("%018llu", val[i]);
            else if (val[i])
                printf("%llu", val[i]), flag = true;
        }
    }
} ans;
int main() {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < m; i++)
        for (int j = 0; j < n; j++)
            scanf("%d", &P[i].p[j]), P[i].p[j]--;
    B[0][0] = new perm();
    for (int i = 1; i < n; i++)
        B[i][i] = B[0][0];
    for (int i = 0; i < m; i++)
        sifting(P[i]);
    while (!Qu.empty()) {
        int x = Qu.front().first, y = Qu.front().second;
        Qu.pop();
        for (int i = 0; i < n; i++)
            for (int j = i + 1; j < n; j++)
                if (B[i][j] != NULL) sifting(mul(*B[i][j], *B[x][y], 0));
    }
    for (int i = 0; i < n; i++) {
        int cnt = 0;
        for (int j = i; j < n; j++)
            if (B[i][j] != NULL) cnt++;
        ans = ans * cnt;
    }
    return ans.print(), 0;
}