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>
using namespace std;
int a[10000],count=0,n;

void dfs(int depth,int i,int b[]) {
	b[depth] = a[i];
	if(depth == 3) {
		//count++;
		if(b[1]+b[2]>b[3] && b[3]+b[2]>b[1] && b[3]+b[1]>b[2])
		 count++;
		 return;
	}
	if(i == n)
	 return;
	
	for(int j=1;j<=n-i;j++) {
		dfs(depth+1,i+j,b);
	}
	 return;
}

int main() {
	cin>>n;
	int b[4];
	for(int i=1;i<=n;i++)
	  cin>>a[i];
	  dfs(1,1,b);
	  cout<<count;
	  return 0;
}
*/

#include<iostream>
using namespace std;
int main() {
	int n,a[10000],count=0;
	cin>>n;
	for(int i=1;i<=n;i++)
	  cin>>a[i];
	for(int i=1;i<=n-2;i++)
  for(int j=i+1;j<=n-1;j++)
    for(int k=j+1;k<=n;k++)
      if(a[i]+a[j]>a[k] && a[i]+a[k]>a[j] && a[k]+a[j]>a[i]) {
      	count++;
	  }
	  cout<<count;
	  return 0;
}