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

int main(void) {
    int n,cnt=0;
    scanf("%d",&n);
    int l[n];
    for(int i=0;i<n;i++){
      scanf("%d", &l[i]);
    }
    qsort(l, sizeof(l)/sizeof(int), sizeof(int), so);
    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[k] < l[i] + l[j]) cnt++;
            }
        }
    }
    printf("%d\n", cnt);
    return 0;
}