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 <stdio.h>

#define MAXN 1001
int Stick[MAXN];


int main()
{
#ifdef _WIN32
	freopen("input.txt", "r", stdin);
#endif
	
	int N;
	scanf("%d", &N);

	for (int n = 0; n < N; n++)
		scanf("%d", &Stick[n]);

	for(int i = 0; i < N; i++)
		for(int j = i; j < N; j++)
			if (Stick[i] > Stick[j])
			{
				int Temp = Stick[i];
				Stick[i] = Stick[j];
				Stick[j] = Temp;
			}

	int Result = 0;
	for (int x = 0; x < N; x++)
		for (int y = x + 1; y < N; y++)
			for (int z = y + 1; z < N; z++)
					if (Stick[x] + Stick[y] > Stick[z])
							Result++;

	printf("%d", Result);
}