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.*;
import java.lang.*;

public class A280 {
	public static void main(String[] args) {
		Scanner scan = new Scanner (System.in);
		
		int num = scan.nextInt();
		
		int curr = 0;
		int answer = 0;
		int i = 1;
		while (num > 0) {
			curr = curr + i;
			//System.out.println(curr);
			num -= curr;
			i++;
			//System.out.println(num);
			if (num >= 0) {
				answer++;
			}
		}
		
		System.out.println(answer);
	}
}
