algebra_8

#include <stdio.h>
#include <stack>
#include <math.h>
#include <time.h>
#include <iostream>
#include <algorithm>
#include <string>
#include <set>
#include <iomanip>
#include <vector>
#include <map>
#include <cassert>
#include <queue>
#include <fstream>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef vector<vector<int>> vvint;

#define forn(i, n) for (int i = 0; i < int(n); ++i)
#define pb push_back
#define mp make_pair
#define all(v) v.begin(),v.end()
#define EPS 1e-9
#define PI 3.1415926535897932384626433832795

vector <vector <vector <int>>> F;
int set_size, matrix_size, characteristic;

vvint null;
vvint edin;

int mul(int a, int b) {
    return (a * b) % characteristic;
}

vvint sum(vvint &a, vvint &b) {
    vvint temp(a.size());
    forn (i, a.size()) {
        forn (j, a.size()) {
            temp[i].push_back((a[i][j] + b[i][j]) % characteristic);
        }
    }
    return temp;
}

vvint mul(vvint &a, vvint &b) {
    vvint temp(a.size());
    forn (i, a.size()) {
        forn (j, a.size()) {
            int tek = 0;
            forn (k, a.size()) {
                tek += a[i][j] * b[j][k];
            }
            temp[i].push_back(tek % characteristic);
        }
    }
    return temp;
}



bool condition_1 () {
    forn (i, set_size) {
        forn (j, set_size) {
            if (i != j && sum(F[i], F[j]) != sum(F[j], F[i])) {
                cout << "1) no" << endl;
                return false;
            }
        }
    }
    cout << "1) yes" << endl;
    return true;
}

bool condition_2 () {
    forn (i, set_size) {
        forn (j, set_size) {
            forn (k, set_size) {
                if (i != j && j != k && i != k
                    && sum(sum(F[i], F[j]), F[k]) != sum(F[i], sum(F[j], F[k]))) {
                        cout << "2) no" << endl;
                        return false;
                }
            }
        }
    }
    cout << "2) yes" << endl;
    return true;
}

bool condition_3 () {
    forn (i, set_size) {
        if (sum(null, F[i]) != F[i]) {
            cout << "3) no" << endl;
            return false;
        }
    }
    cout << "3) yes" << endl;
    return true;
}
bool condition_4 () {
    forn (i, set_size) {
        bool f = false;
        forn (j, set_size) {
            if (sum(F[i], F[j]) == null)
                f = true;
        }
        if (!f) {
            cout << "4) no" << endl;
            return false;
        }
    }
    cout << "4) yes" << endl;
    return true;
}
bool condition_5 () {
    forn (i, set_size) {
        forn (j, set_size) {
            if (i != j && mul(F[i], F[j]) != mul(F[j], F[i])) {
                cout << "5) no" << endl;
                return false;
            }
        }
    }
    cout << "5) yes" << endl;
    return true;
}
bool condition_6 () {
    forn (i, set_size) {
        forn (j, set_size) {
            forn (k, set_size) {
                if (i != j && j != k && i != k
                    && mul(mul(F[i], F[j]), F[k]) != mul(F[i], mul(F[j], F[k]))) {
                        cout << "6) no" << endl;
                        return false;
                }
            }
        }
    }
    cout << "6) yes" << endl;
    return true;
}
bool condition_7 () {
    forn (i, set_size) {
        if (mul(F[i], edin) != F[i]) {
            cout << "7) no" << endl;
            return false;
        }
    }
    cout << "7) yes" << endl;
    return true;
}
bool condition_8 () {

    cout << "8) yes" << endl;
    return true;
}
bool condition_9 () {

    cout << "9) yes" << endl;
    return true;
}



int main () {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    cin >> set_size >> matrix_size >> characteristic;

    null.resize(matrix_size);
    edin.resize(matrix_size);
    forn (i, matrix_size) {
        forn (j, matrix_size) {
            null[i].push_back(0);
            if (i == j)
                edin[i].push_back(1);
            else
                edin[i].push_back(0);
        }
    }

    forn (i, set_size) {
        vvint ttmp;
        forn (j, matrix_size) {
            vector <int> tmp(matrix_size);
            forn (k, matrix_size) {
                cin >> tmp[k];
            }
            ttmp.push_back(tmp);
        }
        F.push_back(ttmp);
    }
    condition_1();
    condition_2();
    condition_3();
    condition_4();
    condition_5();
    condition_6();
    condition_7();
    condition_8();
    condition_9();
    cout << clock() << " ms";
    return 0;
}



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25 2 5
0 0 0 0
1 0 0 1
2 0 0 2
3 0 0 3
4 0 0 4
0 4 1 4
1 4 1 0
2 4 1 1
3 4 1 2
4 4 1 3
0 3 2 3
1 3 2 4
2 3 2 0
3 3 2 1
4 3 2 2
0 2 3 2
1 2 3 3
2 2 3 4
3 2 3 0
4 2 3 1
0 1 4 1
1 1 4 2
2 1 4 3
3 1 4 4
4 1 4 0