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: Accepted)

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>

using namespace std;

int main() {
  int n;
  cin >> n;
  vector<int> L(n);
  for (int i = 0; i < n; i++) {
    cin >> L[i];
  }
  sort(L.begin(), L.end());
  int64_t ans = 0;
  for (int i = 0; i < n; i++) {
    const int a = L[i];
    for (int j = i + 1; j < n; j++) {
      const int b = L[j];
      for (int k = j + 1; k < n; k++) {
        if (L[k] >= a + b) continue;
        const int c = L[k];
        if (a < b + c && b < c + a) ++ans;
      }
    }
  }
  cout << ans << endl;
  return 0;
}