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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int compare_int(const void *a, const void *b) {
    return *(int*)a - *(int*)b;
}

unsigned long max(unsigned long x, unsigned long y) {
    if(x > y) return x;
    return y;
}
unsigned long min(unsigned long x, unsigned long y) {
    if(x < y) return x;
    return y;
}

int main() {
    int N;
    scanf("%d", &N);
    int i;
    int *l = (int*)malloc(N * sizeof(int));
    for(i=0; i<N; i++) {
        scanf("%d", &l[i]);
    }
    qsort(l, N, sizeof(int), compare_int);

    int count = 0;
    int a, b, c;
    for(a=0; a<N; a++) {
        for(b=a+1; b<N; b++) {
            for(c=b+1; c<N; c++) {
                if(l[a] < l[b] + l[c] && l[b] < l[a] + l[c] && l[c] < l[a] + l[b]) {
                    count++;
                }
            }
        }
    }
    printf("%d\n", count);
    free(l);
    return 0;
}