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>
int conbination(int n,int r);
int main(){
    int n;
    int l[2001];
    scanf("%d",&n);
    int i;
    for(i=1;i<=n;i++){
        scanf("%d",&l[i]);
    }
    int j,k;
    int count = 0;
    for(i=1;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){
                    count++;
                }
            }
        }
    }
    printf("%d\n",count);
    return 0;
}
int conbination(int n,int r){
    if(r == 0 || r == n){
        return 1;
    }
    else if(r == 1){
        return n;
    }
    else{
        return conbination(n-1,r-1)+conbination(n-1,r);
    }
}