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>
#define ROOP(i, N) for(int i=0; i++; i<N)
#define RVROOP(i, N) for(int i=N; i--; i>=0)
#define INF 1e9
#define ALL(v) v.begin(), v.end()
using namespace std;
typedef long long ll;

int main() {
  int N; cin>>N;

  vector<int> L(N); 
  for(int i=0; i<N; i++){
    cin>>L.at(i);
  } 

  sort(L.begin(), L.end());
  
  int ans=0;

  for(int i=N-1; i>0; i--){
    for(int j=i-1; j>0; j--){
      for(int k=j-1; k>=0; k--){
        if(L.at(k)+L.at(j)>L.at(i)){
          ans++;
        }
        else{
          break;
        }
      }
    }
  }

  cout<<ans<<endl;
  
  return 0;
}