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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
int main(){
    int n;
    scanf("%d",&n);
    int l[n];
    for(int i = 0;i<n;i++){
        scanf("%d",&l[i]);
    }

    int tmp;
    for(int i = 0;i < n;i++){
        for(int j = 1;j < n;j++){
            if(l[j] < l[j - 1]){
                tmp = l[j];
                l[j] = l[j - 1];
                l[j - 1] = tmp;    
            }
        }
    }
    int ind;
    int count = 0;
    for(int i = 0;i<(n - 2);i++){
        ind = 2;
        for(int j = (i+1);j<(n - 1);j++){
            ind = j + 1;
            while(1){
               
                if(n == ind){
                    break;
                }
                 ind++;
                if(l[ind] > (l[i] + l[j])){
                    count += (n - ind);
                    break;
                }

            }
        }
        printf("%d",count);
        return 0;
    }
    printf("%d",count);
    return 0;
}