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>
#include <string.h>

int main(){

	long int N,cnt=0,tmp=1;
	int L[2010];
	long int i,j,k;
	scanf("%ld",&N);
	
	for(i=0;i<N;i++)scanf("%d",&L[i]);
	

	#if 1
	// tmp x x x i 
	//           tmp x x x x
	for(i=0;i<N-2;i++){
		
	for(j=i+1;j<N-1;j++){
		
	for(k=j+1;k<N;k++){
		if( (L[i]<L[j]+L[k]) &&(L[j]<L[k]+L[i])&&(L[k]<L[j]+L[i]) ) cnt++;
		//printf("%ld,",tmp++);
	}
	}
	}
	#endif
	
	printf("%ld\n",cnt);
	return 0;
 }