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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>

int cmp(const void *a, const void  *b) {
  return *(int*)b - *(int*)a;
}
int main(void) {
  int n, ans = 0;
  scanf("%d", &n);
  
  int l[n];
  for (int i = 0; i < n; i++) scanf("%d", &l[i]);
  
  qsort(l, n, sizeof(int), cmp);
  
  for (int i = 0; i < n; i++) {
    for (int j = i+1; j < n; 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])) ans++;
        while(1){
          if(k==n-1 || l[k]!=l[k+1]) break;
          k++;
        }
      }
      while(1){
        if(j==n-1 || l[j]!=l[j+1]) break;
        j++;
      }
    }
    while(1){
      if(i==n-1 || l[i]!=l[i+1]) break;
      i++;
    }
  }
  
  printf("%d", ans);
  return 0;
}