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>
#include<string.h>

int main()
{
    int pParam[2000];
    int num = 0;
    int i, j, k;
    int count = 0;
    int a, b, c;
    
    // スペース区切りの整数の入力
    scanf("%d",&num);
    //pParam = malloc( sizeof(int)*num);
    
    for(i = 0;i < num; ++i){
        scanf("%d", &pParam[i]);
    }
    
    for(i = 0;i < num; ++i){
        for(j = i+1;j < num; ++j){
            for(k = j+1;k < num; ++k){
                
                a = pParam[i];
                b = pParam[j];
                c = pParam[k];
                
                if( !(a < (b+c))){
                    continue;
                }
                if( !(b < (c+a))){
                    continue;
                }
                if( !(c < (a+b))){
                    continue;
                }
                //if( (a < (b+c)) && (b < (c+a)) && (c < (a+b)) ){
                //    ++count;
                //}
                ++count;
                
                //printf("%d %d %d\n", i,j,k);
                
            }
        }
    }
    
    printf("%d",count);
    //free(pParam);
    
    return 0;
}