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 9.2.1) (judge verdict: Time Limit Exceeded)

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

int main()
{

    int N;
    int sum=0;
    int i;
    int j;
    int m;
    scanf("%d",&N);
    int L[N];
    for(i=0;i<N;i++)
    {
        scanf("%d",&L[i]);
    }
    for(i=0;i<N-2;i++)
    {
        for(j=i+1;j<N-1;j++)
        {
           for(m=j+1;m<N;m++)
           {
               if(L[i]<L[j]+L[m]&&L[j]<L[i]+L[m]&&L[m]<L[j]+L[i])
               {
                      sum++;
               }

           }
        }

    }
    printf("%d",sum);
    return 0;
}