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>

int main(){
  int f=1,i,j,k,l,n,m=0,a,b[2005];
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&b[i]);
  }
  i=1;
  while(f==1){
    f=0;
    for(j=0;j<n-i;j++){
      if(b[j]>b[j+1]){
        a=b[j];
        b[j]=b[j+1];
        b[j+1]=a;
        f=1;
      }
    }
    i++;
  }
  for(i=n-1;i>=2;i--){
    for(j=i-1;j>=1;j--){
      l=b[i]-b[j];
      for(k=j-1;k>=0;k--){
        if(b[k]<=l){
          break;
        }else{
          m++;
        }
      }
    }
  }
  printf("%d",m);
  return(0);
}