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;

//使用する配列の最大要素数
#define MAX_SIZE_N 2000
//使用する変数の宣言と初期化
int a=0,b=0,c=0,n;
int L[MAX_SIZE_N]={0};
int result=0;

int main()
{
  cin >> n;
  for(int i=0;i<n;++i) cin >> L[i];
  sort(L, L + n);

  //処理
  for(int i=0;i<n-2;i++){
    for(int j=i+1;j<n-1;j++){
      for(int k=j+1;k<n;k++){
        if(L[i]<L[j]+L[k] && L[j]<L[k]+L[i] && L[k]<L[i]+L[j] ) result++;
        else break;
      }
    }
  }    
  
  cout << result;
    
  return 0;
}