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 L[1000];
int main()
{
    int N,i=0;//i为记录构成的三角形的个数
    scanf("%d",&N);
    getchar();
    for(int n=0;n<N;n++){
            scanf("%d",&L[n]);
    }
    for(int a=0;a<N-2;a++){
            for(int b=a+1;b<N-1;b++){
                    for(int c=b+1;c<N;c++){
                            if(L[a]+L[b]>L[c]&&L[a]+L[c]>L[b]&&L[b]+L[c]>L[a]){
                                    i++;
                            }
                    }
            }
    }
    printf("%d",i);
    return 0;
}