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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
#define rep(i, n)for(int i=0; i<n; i++)

int main(){
  int N;
  cin >> N;
  vector<int> L(N);
  rep(i, N)
    cin >> L[i];
  //

  sort(L.begin(), L.end());

  long long ans = 0;
  for(int i=0; i<N-2; i++){
    for(int j=i+1; j<N-1; j++){
      int sum = L[i] + L[j];
      int right = upper_bound(L.begin()+j, L.end(), sum-1) - L.begin();
      ans += (right-1 - j);
    }
  }
  
  cout << ans << endl;

  return 0;
}