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
143
144
145
146
147
148
149
150
#include <iostream>
#include <vector>
#include <algorithm>
#include <unordered_map>
#include <cassert>

using namespace std;

const bool DBG = false;
const bool DBG2 = false;

unordered_map<int, int> U, D;
long long zera;

long long solve() {
  long long result = 0;
  if (zera >= 3) {
    result += zera * (zera - 1) * (zera - 2) / 6;
    if (DBG) {
      cout << " 3 zera " << zera << " => " << result << endl;
    }
  }
  if (U.size() == 0 || D.size() == 0) {
    return result;
  }
  for (auto u1 = U.begin(); u1 != U.end(); ++u1) {
    if (zera) {
      int d = -u1->first;
      auto it = D.find(d);
      if (it != D.end()) {
	auto cnt = (long long) u1->second * zera * it->second;
	result += cnt;
	if (DBG) {
	  cout << u1->first << '[' << u1->second
	    << "] + 0[" << zera
	    << "] + " << d << '[' << it->second << "] => "
	    << cnt << '\n';
	}
      }
    }
    for (auto u2 = u1; u2 != U.end(); ++u2 ) {
      if (u2 == u1) {
	int d = -2*u1->first;
	auto it = D.find(d);
	if (it != D.end()) {
	  auto cnt = (long long) u1->second * (u1->second - 1) 
	    * (it->second) / 2;
	  result += cnt;
	  if (DBG) {
	    cout << "2 * " << u1->first << '[' << u1->second
	      << "] + " << d << '[' << it->second << "] => "
	      << cnt << '\n';
	  }
	}
      } else {
	int d = -u1->first - u2->first;
	auto it = D.find(d);
	if (it != D.end()) {
	  auto cnt = (long long) u1->second * (u2->second) * it->second;
	  result += cnt;
	  if (DBG) {
	    cout << u1->first << '[' << u1->second << "] + "
	      << u2->first << '[' << u2->second << "] + "
	      << d << '[' << it->second << "] => "
	      << cnt << '\n';
	  }
	}
      }
    }
  }
  return result;
}

long long solve2() {
  long long result = 0;
  if (U.size() == 0 || D.size() == 0) {
    return result;
  }
  for (auto u1 = U.begin(); u1 != U.end(); ++u1) {
    for (auto u2 = u1; u2 != U.end(); ++u2 ) {
      if (u2 == u1) {
	int d = -2*u1->first;
	auto it = D.find(d);
	if (it != D.end()) {
	  auto cnt = (long long) u1->second * (u1->second - 1) 
	    * (it->second) / 2;
	  result += cnt;
	  if (DBG) {
	    cout << "2 * " << u1->first << '[' << u1->second
	      << "] + " << d << '[' << it->second << "] => "
	      << cnt << '\n';
	  }
	}
      } else {
	int d = -u1->first - u2->first;
	auto it = D.find(d);
	if (it != D.end()) {
	  auto cnt = (long long) u1->second * (u2->second) * it->second;
	  result += cnt;
	  if (DBG) {
	    cout << u1->first << '[' << u1->second << "] + "
	      << u2->first << '[' << u2->second << "] + "
	      << d << '[' << it->second << "] => "
	      << cnt << '\n';
	  }
	}
      }
    }
  }
  return result;
}

int main() {
  int n;
  cin >> n;
  vector<int> liczby(n);
  for (int i = 0; i < n; ++i) {
    cin >> liczby[i];
  }
  //cout << D.bucket_count() << endl;
  D.reserve(20000);
  U.reserve(20000);
  //cout << D.bucket_count() << endl;
  for (int i = 0; i < n; ++i) {
    int sum = 0;
    for (int j = i; j < n; ++j) {
      sum += liczby[j];
      if (sum > 0) D[sum]++;
      else if (sum < 0) U[sum]++;
      else ++zera;
      if (DBG2) {
	cout << "sum " << sum << " zera " << zera << endl;
      }
    }
    if (DBG) {
      cout << "i " << i << " sizes " << D.size() << ' ' << U.size() << endl;
    }
  }
  long long result;
  if (D.size() < U.size()) {
    swap(D, U);
  }
  //cout << D.bucket_count() << endl;
  //cout << D.size() << endl;
  result = solve();
  swap(U, D);
  result += solve2();
  cout << result << endl;
  return 0;
}