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 <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  
  vector<int> A;
  int a1;
  for ( int i=0; i<N; ++i ) {
    cin >> a1;
    A.push_back(a1);
  }
  int s=0;
  int a,b,c;
  for ( int i=2; i<N; ++i )  {
    a=A.at(i);
    for ( int j=1; j<i; ++j ) {
      b=A.at(j);
      for (int k=0; k<j; ++k ) {
        c=A.at(k);
        if ( ((a<b+c) && (b<c+a)) && (c<a+b) ) s++;
      }
    }
  }
  
  cout << s;
}