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: Accepted)

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

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

int main(void){

    int N,i,j,k,L[2001],s,ans=0,top,under;

    scanf("%d",&N);
    for(i = 0;i < N;i++){
        scanf("%d",&L[i]);
    }

    qsort(L,N,sizeof(int),compare_int);

    for(i = 0;i < N - 2;i++){
        for(j = i + 1;j < N - 1;j++){
            top = N;
            under = j + 1;
            while(under != top){
                int mid = (top + under)/2;
                if(L[mid] < L[i] + L[j]){
                    under = mid + 1;
                }else{
                    top = mid;
                }
            }
            ans += top - j - 1;
        }
    }

    printf("%d\n",ans);
    return 0;
}