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 check(int a,int b,int c) {
    int d=b-c;
    if (d<0) d=(-1)*d;
    if (d<a && a<b+c) return 1;
    else return 0;
}

int main(void) {
    int num,*mat,i,j,k,ans=0;
    scanf("%d",&num);
    mat=malloc(sizeof(int)*num);
    for (i=0;i<num;i++) {
        scanf("%d",&mat[i]);
    }
    for (i=0;i<num-2;i++) {
        for (j=i+1;j<num-1;j++) {
            for (k=j+1;k<num;k++) {
                ans+=check(mat[i],mat[j],mat[k]);
            }
        }
    }
    free(mat);
    printf("%d\n",ans);
    return 0;
}