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>
using namespace std;

int main() {
  int N;
  cin >> N;
  
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a.at(i);

  sort(a.begin(), a.end(), greater<int>());
  
  int sum = N*(N-1)*(N-2)/6;
  for (int i = 0; i < N-2; i++) {
    for (int k = i+1; k < N-1; k++) {
      int b = a.at(i) - a.at(k);
      int x = N;
      for (int l = k+1; l < N; l++) {
        if (a.at(l) <= b) {x = l; break;}
      }
      sum -= N - x;
    }
  }
  
  cout << sum << endl;
}