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: Accepted)

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

typedef long long ll;

int len[2005], n;

int compare(const void * a, const void * b) { 
    return ( *(int*)a - *(int*)b ); 
}

int upper_bound(int x) {
	int lo = 0, hi = n-1, mid, ans = 0;
	while (lo <= hi) {
		mid = (lo+hi)/2;
		if (len[mid] >= x)
			hi = mid-1;
		else {
			ans = mid;
			lo = mid+1;
		}
	}
	return ans;
}

int lower_bound(int x) {
	int lo = 0, hi = n-1, mid, ans = n-1;
	while (lo <= hi) {
		mid = (lo+hi)/2;
		if (len[mid] <= x)
			lo = mid+1;
		else {
			ans = mid;
			hi = mid-1;
		}
	}
	return ans;
}

int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d", &len[i]);
	qsort(len, n, sizeof(int), compare);
	ll ans = 0;
	for (int i = 0; i < n; i++) {
		for (int j = i+1; j < n; j++) {
			int tmp = len[i]+len[j];
			int ub = upper_bound(tmp);
			tmp = len[j]-len[i];
			int lb = lower_bound(tmp);
			ans += ub-lb+1;
			if (lb <= j)
				ans--;
			if (lb <= i)
				ans--;
		}
	}
	printf("%lld\n", ans/3);
	return 0;
}