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: Runtime Error)


// D - Triangles

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int L[1000];

int main(){
	int N;
	cin >> N;

	for (int i=0; i<N; i++) {
		cin >> L[i];
	}

	int ans = 0;
	for (int i=0; i<N-2; i++) {
		for (int j=i+1; j<N-1; j++) {
			for (int k=j+1; k<N; k++) {
				if (L[i] < L[j] + L[k] && L[j] < L[k] + L[i] && L[k] < L[i] + L[j]) ans++;
			}
		}
	}

	cout << ans << endl;

	return 0;
}