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;

typedef signed long long ll;
const int N = 2e3 + 5;
int A[N];

int main() {
	int n;
	scanf("%d", &n);
	for(int i = 0; i < n; scanf("%d", &A[i]), i++);
	sort(A, A + n);
	ll tot = ((ll)n * (ll)(n - 1) * (ll)(n - 2)) / 6;
	for(int i = 0; i < n; i++) {
		for(int j = i + 1; j < n; j++) {
			int cnt = n - (lower_bound(A, A + n, A[i] + A[j]) - A);
			tot -= cnt;
		}
	}
	printf("%lld\n", tot);
	return 0;
}