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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include "bits/stdc++.h"
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

int n, ans, j, k;
int l[2000];
int main() {
	scanf("%d", &n);
	rep(i, n) {
		scanf("%d", &l[i]);
	}
	sort(l, l + n, greater<int>());
	rep(i, n - 2) {
		for (j = i + 1; j < n - 1; ++j) {
			for (k = j + 1; k < n; ++k) {
				if (l[i] - l[j] >= l[k]) break;
				++ans;
			}
		}
	}
	printf("%lld\n", ans);
}