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
#include <bits/stdc++.h>

using namespace std;

#define JOIN_(X, Y) X##Y
#define JOIN(X, Y) JOIN_(X, Y)
#define TMP JOIN(tmp, __LINE__)
#define PB push_back
#define SZ(x) int((x).size())
#define REP(i, n) for (int i = 0, TMP = (n); i < TMP; ++i)
#define FOR(i, a, b) for (int i = (a), TMP = (b); i <= TMP; ++i)
#define FORD(i, a, b) for (int i = (a), TMP = (b); i >= TMP; --i)

#ifdef DEBUG
#define DEB(x) (cerr << x)
#else
#define DEB(x)
#endif

typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;

const ll INF = static_cast<ll>(1e18) + 9;

void inline one() {
    int n;
    cin >> n;
    vi prefix_sum(1, 0);
    REP(i, n) {
        int x;
        cin >> x;
        int sum = prefix_sum.back() + x;
        prefix_sum.PB(sum);
    }
    vi t;
    REP(i, n) {
        FOR(j, i + 1, n) { t.PB(prefix_sum[j] - prefix_sum[i]); }
    }
    unordered_map<int, ll> cnt;
    DEB("t:\n");
    for (int x : t) {
        DEB(x << " ");
        ++cnt[x];
    }
    DEB("\n");
    DEB("cnt:\n");
    ll result = 0;
    vector<pair<int, ll>> pairs;
    for (const auto &[k, v] : cnt) {
        // DEB(k << ": " << v << "\n");
        pairs.emplace_back(k, v);
    }
    DEB("SZ(t)=" << SZ(t) << " SZ(cnt)=" << SZ(cnt) << " SZ(pairs)=" << SZ(pairs) << "\n");
    sort(pairs.begin(), pairs.end());
    FOR(i, 0, SZ(pairs) - 1) {
        auto [a, a_cnt] = pairs[i];
        // DEB("a=" << a << "\n");
        if (a > 0) {
            break;
        }
        // int start = i;
        // int end = SZ(pairs) - 1;
        const auto &ub = upper_bound(pairs.begin() + i, pairs.end(), pair<int, ll>(-2 * a, INF));
        int end = distance(pairs.begin(), ub) - 1;
        const auto &lb = lower_bound(pairs.begin() + i, pairs.end(),
                                     pair<int, ll>(-(a + pairs[end].first), -INF));
        int start = distance(pairs.begin(), lb);
        while (start <= end) {
            auto [b, b_cnt] = pairs[start];
            auto [c, c_cnt] = pairs[end];
            int sum = a + b + c;
            if (sum == 0) {
                if (i == start and start == end) {
                    if (a_cnt >= 3) {
                        result += a_cnt * (b_cnt - 1) * (c_cnt - 2) / 6;
                    }
                } else if (i == start) {
                    if (a_cnt >= 2) {
                        result += (a_cnt * (b_cnt - 1)) / 2 * c_cnt;
                    }
                } else if (start == end) {
                    if (b_cnt >= 2) {
                        result += a_cnt * (b_cnt * (c_cnt - 1)) / 2;
                    }
                } else {
                    result += a_cnt * b_cnt * c_cnt;
                }
                ++start;
                --end;
            } else if (sum > 0) {
                --end;
            } else {
                ++start;
            }
        }
    }
    cout << result << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    // int z; cin >> z; while(z--)
    one();
}