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: Time Limit Exceeded)

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int main(){
  long long n;
  std::cin >> n;
  std::vector<int> l(n);
  for (int i = 0; i < n; i++)std::cin >> l[i];
  sort(l.begin(),l.end());


  int ans=0;
  for (int i = 0; i < n; i++) {
    for (int i2 = 0; i2 < n; i2++) {
      if(i==i2)continue;
      if(l[0]>l[i]+l[i2])break;
      for (int i3 = 0; i3 < n; i3++) {
        if(i==i3 || i2==i3)continue;
        if(l[i3]>l[i]+l[i2])break;
        if(l[i]<l[i2]+l[i3] && l[i2]<l[i]+l[i3] && l[i3]<l[i]+l[i2]){
          ans++;
        }

      }
    }
  }

  std::cout << ans/6 << '\n';



return 0;
}