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: Time Limit Exceeded)

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

//qsort
int asc(const void *a, const void *b) {
  return *(int *)a - *(int *)b;
}
int desc(const void *a, const void *b) {
  return *(int *)b - *(int *)a;
}

int main(void){
    int n;
    scanf("%d",&n);
    int d[n];
    for(int i=0;i<n;i++)scanf("%d",&d[i]);
    qsort(d, n, sizeof(int), asc);
    long long int rslt = 0;

    for(int i=0;i<n-2;i++){
        for(int j=i+1;j<n-1;j++){
            int ij = (d[j]+d[i]);
            for(int k=j+1;k<n;k++){
                if(d[k]>ij)break;
                if((d[i]<(d[j]+d[k]))&&(d[j]<(d[i]+d[k]))&&(d[k]<ij)){
                    rslt += 1;
                }
            }
        }
    }

    printf("%lld\n",rslt);
    return 0;
}