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 (Clang 3.8.0) (judge verdict: Accepted)

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

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

int main(){
	
	int N,L[3000],i,ans=0,j,k;
	scanf("%d",&N);
	
	for(i=0;i<N;i++){
		scanf("%d",&L[i]);
	}
	
	qsort(L,N,sizeof(int),compare);
	
	
	for(i=0;i<N;i++){
		for(j=i+1;j<N;j++){
			for(k=j+1;k<N;k++){
			if((L[i]<L[j]+L[k])&&(L[j]<L[k]+L[i])&&(L[k]<L[i]+L[j])){
				ans++;
			}
			}
		}
	}
	
	
	printf("%d",ans);
	
	return 0;
}