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>

#define IS_TRI(A, B, C) (A < B+C && B < C+A && C < A+B)

int main (void) {
    int i, j, k, scaned;
    int n;
    scaned = scanf("%d", &n);
    if ( scaned != 1 ) {
        fprintf(stderr, "invalid input\n");
        return EXIT_FAILURE;
    }
    int l[n];
    for ( i=0; i<n; i++ ) {
        scaned = scanf("%d", &l[i]);
        if ( scaned != 1 ) {
            fprintf(stderr, "invalid input\n");
            return EXIT_FAILURE;
        }
    }

    long long ans=0;
    for ( i=0; i<n-2; i++ ) {
        for ( j=i+1; j<n-1; j++ ) {
            for ( k=j+1; k<n; k++ ) {
                if ( IS_TRI(l[i], l[j], l[k]) )
                    ans++;
            }
        }
    }

    printf("%lld\n", ans);
    return EXIT_SUCCESS;
}