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>

int main()
{
	int n = 0, s=0;/*num of stick, sum of trinangles*/
  	int l[2000];/*array of stick length*/
  
  	scanf("%d", &n);
 	for(int i=0; i<n; i++)
    {
    	scanf("%d", &l[i]);
    }
  	
  	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++)
            {
				int max;
              	
              	max = l[i] > l[j]?l[i]:l[j];
              	max = max > l[k]?max:l[k];
            	if(max<(l[i]+l[j]+l[k]-max)){
                	s++;
                }
            }
        }
    }
  
  	printf("%d", s);
	return 0;
}