Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1


Output

1


Input

25


Output

4

Note

Illustration to the second sample: 

<image>
import java.util.Scanner;
import java.util.TreeSet;

public class Main{ 
	
     public static void main(String[] args){ 
    	 
		Scanner scan = new Scanner(System.in);		
		
		int n = scan.nextInt();
		
		int sum = 0;
		
		int pf = 0;
		
		int result = 0;
		
		for(int i = 1; ; i++){
			
			pf = pf + i;
			
			sum = sum + pf;
			
			if(sum > n){
				
				result = i - 1;
				break;
			}				
		}
		
		System.out.println(result);
	}
}
















