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
#include <iostream>
#include <list>

using namespace std;

static const int PRIME = 1000000007;

int sum[5000 * 5000 + 1];
int pascal[5001][5001];

class Item {
public:
    int a;
    int c;

    Item(int aa, int cc) : a(aa), c(cc) {}
};

int main() {

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n;
    cin >> n;

    int aa;
    int aSum = 0;
    list<int> input;
    for (int i = 0; i < n; i++) {
        cin >> aa;
        input.emplace_back(aa);
        aSum += aa;
    }

    input.sort();
    list<Item> input2;

    int maxCount = 1;
    int last = -1;
    int lastCount = 0;
    for (auto const a : input) {
        if (last == -1) {
            if(a > 1) {
                cout << 0 << endl;
                return 0;
            }
            input2.emplace_back(Item(a, 1));
            last = 0;
        } else if (a == last) {
            lastCount++;
            if (lastCount > maxCount) {
                maxCount = lastCount;
            }
        } else {
            if (last > 0) {
                input2.emplace_back(Item(last, lastCount));
            }
            last = a;
            lastCount = 1;
        }
    }
    input2.emplace_back(Item(last, lastCount));

//    int *sum = new int[aSum + 1]();
//    int **pascal = new int *[maxCount+1];
//    pascal[0] = new int[1];
    pascal[0][0] = 1;

    for (int i = 1; i <= maxCount; i++) {
//        pascal[i] = new int[i + i];
        pascal[i][0]=1;
        pascal[i][i]=1;
        for(int j = 1; j < i; j++) {
            pascal[i][j] = (pascal[i-1][j-1]+pascal[i-1][j]) % PRIME;
        }
    }

    sum[0] = 1;

    int maxSum = 0;
//    int ii = 0;
    for (auto const item : input2) {
        int a = item.a;
        int count = item.c;
//        cout << ii++ << endl;
        if (maxSum == 0) {
            maxSum = a;
            sum[a] = 1;
        } else {
            for (int i = maxSum; i >= a - 1; i--) {
                for (int j = 1; j <= count; j++) {
                    sum[i + (count - j + 1) * a] =
                            (sum[i + (count - j + 1) * a] + (int) (((long long) pascal[count][j-1]) * ((long long)sum[i]) % ((long long)PRIME))) % PRIME;
                }
                if (i + count * a > maxSum) {
                    maxSum = i + count * a;
                }
            }
        }
    }

    int result = 0;
    for (int i = 1; i <= maxSum; i++) {
        result = (result + sum[i]) % PRIME;
    }

    cout << result << endl;

    return 0;
}