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: Time Limit Exceeded)

#include <stdio.h>

int main() {
	int N;
	int L[2000];
	int i, j, t;
	int a, b, c;
	int A, B, C;
	int ma;
	int cnt = 0;
	scanf("%d", &N);

	for(i = 0; i < N; i++) {
		scanf("%d", &L[i]);
	}

	for(i = 0; i < N - 1; i++) {
		for(j = i + 1; j < N; j++) {
			if(L[i] > L[j]) {
				t = L[i];
				L[i] = L[j];
				L[j] = t;
			}
		}
	}
	
	for(a = 0; a < N; a++) {
		A = L[a];
		for(b = a+1; b < N; b++) {
			B = L[b];
			ma = A + B;
			for(c = b+1; c < N; c++) {
				if(a == c || c == b) continue;
				C = L[c];
				if(C >= ma) break;
				if(A < B + C && B < C + A && C < A + B) {
					cnt++;
				}
			}
		}
	}

	printf("%d\n", cnt);
	return 0;
}