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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; i++);
using namespace std;

int N, l, ans = 0;

int main() {
  scanf("%d", &N);
  vector<int> v(N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &l);
    v.at(i) = l;
  }
  sort(v.begin(), v.end());

  for (int b = 0; b < N; b++) {
    int r = b + 1;
    for (int a = 0; a < b; a++) {
      int ab = v.at(a) + v.at(b);
      while (r < N && v.at(r) < ab) ++r;
      int l = b + 1;
      ans += max(0, r - l);
    }
  }

  printf("%d\n", ans);
  return 0;
}

// 4 3 4 2 1 1
// 3 1 1000 1 0
// 7 218 786 704 233 645 728 389 23