Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <iostream>
//#include <algorithm>
// #include <iomanip>

using namespace std;

int main() {
  int n;
  scanf("%d", &n);

  vector<int> l(n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &l[i]);
  }
  sort(l.begin(), l.end());

  if (l[0] == l[n - 1]) {
    if (l[0] > 0) {
      cout << n * (n - 1) * (n - 2) / 6 << endl;
    } else {
      cout << 0 << endl;
    }
    return 0;
  }

  int count = 0;
  for (int i1 = 0; i1 < n - 2; i1++) {
    for (int i2 = i1 + 1; i2 < n - 1; i2++) {
      int a = l[i1];
      int b = l[i2];

      auto it1 = lower_bound(l.begin(), l.end(), max((a - b - 1), (b - a - 1)));
      int index1 = it1 - l.begin();

      auto it2 = upper_bound(l.begin(), l.end(), (a + b));
      int index2 = it2 - l.begin();

      int start = max(index1, i2 + 1);
      for (int i = start; i < min(index2, n); i++) {
        int c = l[i];
        if (c > a - b && c > b - a && c < a + b) {
          count++;
        }
      }
    }
  }

  cout << count << endl;
}