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 compare(const void *a,const void *b){
    return *(int*)b-*(int*)a;
}

main(){
  int n, s;
  scanf("%d", &n);
  int L[n];
  for(int i=0; i<n; i++) scanf("%d", &L[i]);
  
  qsort(L,n,sizeof(int),compare);
  
  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]){
          s++;
        }
        else break;
      }
    }
  }
  printf("%d", s);
  return 0;
}