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 int long long
using namespace std;

signed main() {
  int N;
  cin >> N;
  
  vector<int> L(N);
  vector<int> total(3010, 0);
  for( int i = 0; i < N; i++ ){
    cin >> L.at(i);
    total.at(L.at(i))++;
  }
  
  for( int i = 1; i <= 3000; i++ ){
    total.at(i) += total.at(i-1);
  }
  
  int ans = 0;
  int A, B;
  sort(L.begin(), L.end());
  for( int i = 0; i < N; i++ ){
    A = L.at(i);
    for( int j = i+1; j < N; j++ ){
      B = L.at(j);
      ans += total.at(A+B-1) - total.at(B-A);
      if( B-A <A && A <= A+B-1 ) ans--;
      if( B-A < B && B <= A+B-1 ) ans--;
    }
  }
  cout << ans / 3 << endl;
    
}