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 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
int main(){
  int compare_int(const void *a, const void *b)
{
    return *(int*)a - *(int*)b;
}
  int n;
  int l[2000];
  int ans=0;
  scanf("%d",&n);
  for(int i=0;i<n;i++){
    scanf("%d",&l[i]);
  }
  qsort(l, n, sizeof(int), compare_int);
  for(int i=2;i<n;i++){//maxの辺
    for(int j=0;j<i-1;j++){//下の候補
      for(int k=j+1;k<i;k++){//範囲増やすマン
        if(l[j]+l[k]>l[i]){
        ans=ans+i-k;
        //printf("i=%d j=%d ans=%d\n",i,j,ans);
        break;
        }
      }
    }
  }
  
  printf("%d",ans);
  return 0;
}