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 main()
{
    int N,re = 0;
    int l[2000];
    scanf("%d",&N);
    for(int i = 0;i < N;i++)scanf("%d",&l[i]);
    for(int a = 0;a < (N-1);a++)
    {
        for(int b = 0;b < (N-1);b++)
        {
            if(a >= b)continue;
            if(b == 0)b += a;
            for(int c = 0;c < N;c++)
            {
                if(b >= c)continue;
                if(c == 0)c += b;
                if(l[a] < l[b] + l[c] && l[b] < l[a] + l[c] && l[c] < l[a] + l[b])re++;
            }
        }
    }
    printf("%d",re);
    return 0;
}