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>

int main()
{
	int i, N, L[2001];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%d", &(L[i]));
		
	int j, k, l;
	long long count[1001] = {};
	for (i = 1; i <= N; i++) count[L[i]]++;
	
	long long ans = 0, tmp[3];
	for (i = 1; i <= 1000; i++) {
		if (count[i] == 0) continue;
		tmp[0] = count[i]--;
		for (j = i; j <= 1000; j++) {
			if (count[j] == 0) continue;
			tmp[1] = count[j]--;
			l = (i + j - 1 < 1000)? i + j - 1: 1000;
			for (k = j; k <= l; k++) {
				if (count[k] == 0) continue;
				tmp[2] = tmp[0] * tmp[1] * count[k];
				if (i == j || j == k) tmp[2] /= 2;
				if (i == j && j == k) tmp[2] /= 3;
				ans += tmp[2];
			}
			count[j]++;
		}
		count[i]++;
	}
	
	printf("%lld\n", ans);
	fflush(stdout);
	return 0;
}