1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
// drz-drzewa-rozpinajace.cpp : This file contains the 'main' function. Program execution begins and ends there.
//

#include <iostream>
#include <vector>
#include <algorithm>

constexpr int MAXN = 5007;
constexpr long long MD = 1e9 + 7;


long long mat[MAXN][MAXN];

std::vector<long long> dv[MAXN];
int n;

long long ppow(long long a, long long e) {
    long long b = 1;
    while (e > 0) {
        if (e % 2 == 1) {
            b *= a;
            b %= MD;
        }
        e /= 2;
        a *= a;
        a %= MD;
    }
    return b;
}

long long prev(long long a) {
    return ppow(a, MD - 2);
}

long long det() {
    long long res = 1;
    long long rv;
    int k;
    for (int i = 0; i < n; i++) {
        k = i;
        for (int j = i + 1; j < n; j++) {
            if (mat[j][i] != 0) {
                k = j;
            }
        }
        if (mat[k][i] == 0) {
            return 0;
        }
        std::swap(mat[i], mat[k]);
        if (i != k) {
            res = MD - res;
        }
        res = ((res * mat[i][i]) % MD + MD) % MD;
        rv = prev(mat[i][i]);
        for (int j = i + 1; j < n; j++) {
            mat[i][j] *= rv;
            mat[i][j] %= MD;
        }
        for (int j = 0; j < n; j++) {
            if (i != j && mat[j][i] != 0) {
                for (int k = i + 1; k < n; k++) {
                    mat[j][k] = (mat[j][k] - (mat[i][k] * mat[j][i]) % MD + MD) % MD;
                }
            }
        }
    }
    return res;
}

int main()
{
    std::ios_base::sync_with_stdio(0);
    std::cin.tie(0);
    std::cout.tie(0);

    long long l;
    std::cin >> n;

    for (int i = 0; i < n; i++) {
        std::cin >> l;
        for (long long j = 2; l > 1; j++) {
            while (l % j == 0) {
                l /= j;
                dv[i].push_back(j);
            }
        }
    }

    std::vector<long long> v_intersection;
    

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (i == j) {
                continue;
            }
            v_intersection.clear();
            std::set_intersection(dv[i].begin(), dv[i].end(), dv[j].begin(), dv[j].end(), std::back_inserter(v_intersection));
            mat[i][j] = -1;
            for (auto u : v_intersection) {
                mat[i][j] *= u;
            }
            mat[i][i] -= mat[i][j];
        }
    }

    n--;
    /*
    for (int i = 0; i < n; i++) {
        std::cout << "{";
        for (int j = 0; j < n; j++) {
            std::cout << mat[i][j] << ',';
        }
        std::cout << "}, ";
    }
    */
    std::cout << det() % MD << '\n';
}

// Run program: Ctrl + F5 or Debug > Start Without Debugging menu
// Debug program: F5 or Debug > Start Debugging menu

// Tips for Getting Started: 
//   1. Use the Solution Explorer window to add/manage files
//   2. Use the Team Explorer window to connect to source control
//   3. Use the Output window to see build output and other messages
//   4. Use the Error List window to view errors
//   5. Go to Project > Add New Item to create new code files, or Project > Add Existing Item to add existing code files to the project
//   6. In the future, to open this project again, go to File > Open > Project and select the .sln file