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 (Clang 3.8.0) (judge verdict: Accepted)

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

int canmaketriangle(int a, int b, int c);

int main()
{
  int n;
  int* l;
  int c = 0;
  scanf("%d", &n);
  l = (int*)malloc(n);
  if (l == NULL)
    return -1;
  for (int i = 0; i < n; i++)
    scanf("%d", &l[i]);
  for (int i = 0; i < n - 2; i++)
    for (int j = i + 1; j < n - 1; j++)
      for (int k = j + 1; k < n; k++)
        if (canmaketriangle(l[i], l[j], l[k]))
          c++;
  printf("%d", c);
  return 0;
}

int canmaketriangle(int a, int b, int c)
{
  if (a < b + c && b < a + c && c < a + b)
    return 1;
  else
    return 0;
}