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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
using namespace std;

#define rep(i, n) for(int i = 0;i < n;i++)


int main() {

  int n;
  cin >> n;
  int l[2000];
  rep(i, n) {
    cin >> l[i];
  }

  int ans = 0;
  rep(i, n) {
    for (int j = i+1; j < n; j++) {
      for (int k = j+1; k < n; k++) {
        if (l[i] < l[j] + l[k] &&
            l[j] < l[i] + l[k] &&
            l[k] < l[i] + l[j]) {
          ans++;
        }
      }
    }
  }
  cout << ans << endl;
}