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 <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

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

int n;
int l[2000];
int bs(int k, int s, int r){
	while(s<=r){
		int m=(s+r)/2;
		if(l[m]>=k) r=m-1;
		else s=m+1;
	}
	return s;
}

int main(void){
	int i, j;
	scanf("%d", &n);
	for(i=0; i<n; i++){
		scanf("%d", l+i);
	}
	qsort(l, n, sizeof(int), comp);
	long ans=0;
	for(i=0; i<n; i++){
		for(j=0; j<n; j++){
			if(i==j) continue;
			int a=(l[i]>l[j]?l[i]-l[j]:l[j]-l[i]);
			int b=l[i]+l[j];
			if(a+2>b) continue;
			int now=bs(b, 0, n-1)-bs(a+1, 0, n-1);
			if(a<l[i] && l[i]<b) now--;
			if(a<l[j] && l[j]<b) now--;
			//printf("%d %d %d\n", a, b, now);
			ans+=now;
		}
	}
	printf("%ld\n", ans/6);
}