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<bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> vec(N);
  for(int i=0; i<N; i++){
    cin >> vec.at(i);
  }
  sort(vec.begin(),vec.end());
  int cnt = 0;
  for(int i=0; i<N-2; i++){
    for(int j=i+1; j<N-1; j++){
      int x = vec.at(i) + vec.at(j);
      for(int k=j+1; k<N; k++){
        if(x <= vec.at(k)){
          break;
        }
        cnt++;
      }
    }
  }
  cout << cnt << endl;
}