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: Wrong Answer)

// ABC 143-D
// 2019.10.19 bal4u

#include <stdio.h>
#include <stdlib.h>

#if 1
int getchar_unlocked(void);
#define gc() getchar_unlocked()
#else
#define gc() getchar()
#endif

int in() {   // 非負整数の入力
	int n = 0, c = gc();
	do n = 10 * n + (c & 0xf); while ((c = gc()) >= '0');
	return n;
}

void Qsort(int *a, int l, int r) {
	int i, j, m, t;
	
	i = l, j = r, m = a[(l+r) >> 1];
	while (1) {
		while (a[i] < m) i++;
		while (m < a[j]) j--;
		if (i >= j)	break;
		t = a[i], a[i] = a[j], a[j] = t;
		i++, j--;
	}
	if (l+1 < i) Qsort(a, l, i-1);
	if (j+1 < r) Qsort(a, j+1, r);
}

int L[2005];

int main()
{
	int i, j, k, N, ans;
	
	N = in();
	for (i = 1; i <= N; ++i) L[i] = in();
	Qsort(L, 1, N);
	ans = 0;
	for (i = 1; i <= N; ++i) if (L[i] != L[i-1]) {
		for (j = i+1; j <= N; ++j) {
			for (k = j+1; k <= N; ++k) {
				if (L[i] + L[j] > L[k]) ans++;
			}
		}
	}
	printf("%d\n", ans);
	return 0;
}