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>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) < (b) ? (a) : (b))

#define scani(i) scanf("%d", &(i))
#define scanc(c) scanf("%c", &(c))
#define scand(d) scanf("%lf", &(d))

#define printi(i) printf("%d", (i))
#define pr printf("\n")

#define NUM (2000)

int main(int argc, char** argv){
    int n, L[NUM];
    scani(n);

    rep(i, n){
        scani(L[i]);
    }

    int a, b, c;
    int sum = 0;

    rep(i, n){
        a = L[i];

        for(int j = i + 1; j < n; j++){
            b = L[j];

            int sab = a - b;
            int aab = a + b;
            for(int k = j + 1; k < n; k++){
                c = L[k];
                if(
                        sab < c &&
                        sab > - c &&
                        aab > c
                        ){

                    sum++;
                }

            }
        }
    }


    printi(sum);
    pr;

    return 0;
}