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>
#include<string.h>
#include<math.h>

#define num_max(p,q)((p)>(q)?(p):(q))
#define num_min(p,q)((p)<(q)?(p):(q))
int cmp(const void *a, const void *b)
{
	return *(int*)a - *(int*)b;//昇順
	 //降順ならreturn *(int*)b - *(int*)a;
}
int hikaku(int a, int b, int c)
{
	if (a+b<=c)return -1;
	if (b+c<=a)return -1;
	if (c+a<=b)return -1;
	return 0;
}
int main()
{
	int N,i,j,k,ans=0;
	scanf("%d", &N);
	int(*L)= (int(*))
		malloc(N * sizeof(int));
	for (i = 0;i < N;i++)scanf("%d", &L[i]);
	for (i = 0;i < N;i++)
	{
		for (j = i+1;j < N;j++) {
			for (k = j + 1;k < N;k++)
			{
				if (hikaku(L[i], L[j], L[k]) == 0)ans++;
			}
		}
	}
	printf("%d\n", ans);
	free(L);
	return 0;
}