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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Vanya_and_Cubes {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		System.out.println(function(n));
	}
	public static int function(int n) {
		int count = 0;
		for(int i = 1; true ;++i) {
			n = n - fibonacci(i);
			if(n >= 0)count++;
			else {
				break;
			}
		}
		return count;
	}
	public static int fibonacci(int n) {
		int sum = 0;
		for(int i = 1; i <= n; ++i ) {
			sum = sum+i;
		}
		return sum;
	}
}
