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: Runtime Error)

#include <bits/stdc++.h>

using namespace std;

int main() {
	int n;
	int a[1005];
	cin>>n;
	for (int i = 0; i < n; i++)
		cin>>a[i];
	sort(a, a + n);
	/*for (int i = 0; i < n; i++)
		cout<<a[i]<<" ";
	cout<<endl;*/
	int res = 0;
	for (int i = 0; i < n; i++)
	for (int j = i + 1; j  + 1 < n; j++) { //[j + 1 ... n) 
		int l = j + 1, r  = n, m = 0;
		while (r - l > 1) {
			m = (l + r) / 2;
			if (a[m] >= a[i] + a[j]) r = m; else l = m;
		}
		if (a[i] + a[j] > a[j + 1]) {
			res += l - j;
			//cout<<i<<" "<<j<<" "<<(j + 1)<<endl;	
		}
	}
	cout<<res;
}