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: Wrong Answer)

#include <stdio.h>

int is_triangle(int x, int y, int z)
{
  if(x >= y + z) {
    return 0;
  }
  else if(y >= z + x) {
    return 0;
  }
  else if(z >= x + y) {
    return 0;
  }
  else {
    return 1;
  }
}

int merge_sort(int l, int r, int *a)
{
  int k = (r + l) / 2;
  int x, y, z;
  int temp_a[10000];

  if(l >= r - 1) {
    return 0;
  }
  else {
    merge_sort(l, k, a);
    merge_sort(k, r, a);

    x = l;
    y = k;
    z = 0;

    while(z < r-l) {
      if(x >= k) {
        temp_a[z] = a[y];
        y++;
      }
      else if(y >= r) {
        temp_a[z] = a[x];
        x++;
      }
      else if(a[x] < a[y]) {
        temp_a[z] = a[x];
        x++;
      }
      else {
        temp_a[z] = a[y];
        y++;
      }
      z++;
    }

    for(int i = l; i < r; i++) {
      a[i] = temp_a[i-l];
    }

    return 0;
  }
  
}

int main(void)
{
  int n;
  scanf("%d", &n);
  int len[n];
  for(int i = 0;i < n;i++) {
    scanf("%d", &len[i]);
  }
  merge_sort(0, n, len);
  for(int i = 0;i < n;i++) {
    printf("%d ",len[i]);
  }
  printf("\n");

  int sum = 0;
  for(int i = 0; i < n; i++) {
    for(int j = i+1; j < n; j++) {
      for(int k = j+1; k < n; k++) {
        if(is_triangle(len[i],len[j],len[k])) {
          sum++;
        }
        else {
          continue;
        }
      }
    }
  }

  printf("%d\n", sum);

  return 0;
}