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<stdlib.h>
int desc(const void *a, const void *b) { //クイックソート
  return *(int *)a - *(int *)b;
}
int conbination(int n,int r);
int main(){
    int n;
    int l[2001];
    scanf("%d",&n);
    int i,j;
    for(i=0;i<n;i++){
        scanf("%d",&l[i]);
    }
     //qsort(l, n, sizeof(int), desc);
     	for(int i = 0; i < n; i++)
		for(int j = i; j < n; j++)
			if (l[i] > l[j])
			{
				int Temp = l[i];
				l[i] = l[j];
				l[j] = Temp;
			}
 
    // for(i=0;i<n;i++){
        //printf("%d ",l[i]);
  //  }
    int k;
    int count = 0;
    for(i=0;i<n-2;i++){
        for(j=i+1;j<n-1;j++){
            for(k=j+1;k<n;k++){
                int a = l[i],b = l[j],c = l[k];

                if(a < b+c && b < a+c && c < a+b){
                   if(k==n-1){
                         count += k-(j+1)+1;
                   }
                }
                else{
                    count += k-(j+1);
                    break;
                }
                
            }
        }
    }
    printf("%d\n",count);
    return 0;
}