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
130
131
132
133
134
135
136
137
138
139
140
141
142
#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <numeric>
#include <algorithm>

//#include "brut.cpp"

using namespace std;

constexpr int MOD = 1000000007;

int solution(std::vector<int> input) {
    int subsets_ok = 0;

    map<int, int> possible_sets_for_sum;

    possible_sets_for_sum[0] = 1;

    for(auto x: input) {
        vector<pair<int, int>> to_modify;
        auto it = possible_sets_for_sum.lower_bound(x-1);
        while (it != possible_sets_for_sum.end()) {
//            printf("(%d + %d) += %d\n", it->first, x, possible_sets_for_sum[it->first]);
            to_modify.emplace_back(make_pair(it->first + x, it->first));
            it++;
        }
        reverse(to_modify.begin(), to_modify.end());
//        printf("\n");

        for (auto x: to_modify) {
            possible_sets_for_sum[x.first] += possible_sets_for_sum[x.second];
            possible_sets_for_sum[x.first] %= MOD;
        }
    }

    int subsets = 0;
    for(auto y: possible_sets_for_sum) {
        subsets += y.second;
//        cout << "(" << y.first << ", " << y.second << ")" << endl;
    }

//    cout << subsets-1 << endl;

    return subsets-1;
}
using ull = unsigned long long;

int possible_sets_for_sum[5000*5000+100];
int solution2(std::vector<int> input) {
    int subsets_ok = 0;

    std::set<int> keys;

    possible_sets_for_sum[0] = 1;
    keys.insert(0);

    auto keys_it = keys.begin();

    for(auto x: input) {
        while (*keys_it < x-1) {
            keys_it++;
            if (keys_it == keys.end()) {
                break;
            }
        }
        if (keys_it == keys.end()) {
            break;
        }

        auto it = keys.end();
        auto last = keys_it;
        while (it != last) {
            it--;
//            printf("[%d + %d] += [%d]\n", *it, x, *it);

            if (possible_sets_for_sum[*it + x] == 0) {
                keys.insert(*it+x);
            }
            possible_sets_for_sum[*it + x] += possible_sets_for_sum[*it];
            possible_sets_for_sum[*it + x] %= MOD;
        }
//        printf("\n");
    }

    int subsets = 0;
    for(auto y: keys) {
        subsets += possible_sets_for_sum[y];
        subsets %= MOD;
//        cout << "(" << y.first << ", " << y.second << ")" << endl;
    }

//    cout << subsets-1 << endl;

    return subsets-1;
}

//int main() {
//    srand(time(0));
//
//    while(true) {
//        int length = 2 + (rand() % 10);
//        std::vector<int> task;
//
//        task.push_back(1);
//        for (int i = 1; i < length; ++i) {
//            task.push_back(1 + rand() % 5);
//        }
//
//        std::sort(task.begin(), task.end());
//
//        for (auto x: task) {
//            printf("%d, ", x);
//        }
//        printf("\n");
//
//        int a = solution(task);
//        int b = brut(task);
//
//        cout << a << endl << endl;
//        if (a != b) {
//            exit(1);
//        }
//    }
//}

int main() {
    int n;
    cin >> n;
    std::vector<int> task;

    for(int i = 0; i < n; ++i) {
        int a;
        cin >> a;
        task.push_back(a);
    }

    std::sort(task.begin(), task.end());

    cout << solution2(task) << endl;
}