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<string>

using namespace std;


int main(){
  int N;
  int count = 0;
  int L[2001];
  cin >> N;
  for (int i=0;i<N;i++){
      cin >> L[i];
  }

  for (int i =0 ; i <N-2 ;i++){
	for(int j=i+1; j<N-1; j++){
		for ( int z = j+1; z < N; z++){
			if( (L[i] < L[j]+L[z])
			    && (L[j] < L[i]+L[z])
			    && (L[z] < L[i]+L[j]))count++;
		}
	}
   }
   cout << count;
   
   return 0;
}