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

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

int N;
int L[2010];

int main(void) {
  scanf("%d", &N);
  for (int i = 0; i < N; ++i) {
    scanf("%d", &L[i]);
  }
  qsort(L, N, sizeof(int), cmp);

  int ans = 0;
  for (int i = 0; i < N; ++i) {
    for (int j = i + 1; j < N; ++j) {
      int l = j;
      int r = N;
      while (r - l > 1) {
        int c = l + (r - l) / 2;
        if (L[c] >= L[i] + L[j]) {
          r = c;
        } else {
          l = c;
        }
      }
      // printf("%d %d %d %d\n", i, j, l, r);
      ans += l - j;
    }
  }
  printf("%d\n", ans);

  // for (int i = 0; i < N; ++i) {
  //   printf("%d ", L[i]);
  // }
  // puts("");
}