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.*;
public class A {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		long[] ar = new long[10005];
		long[] arr = new long[10005]; 
		ar[1] = 1;
		arr[1]= 1;
		for (int i = 2; i < ar.length; i++) {
			arr[i] = arr[i-1]+i;
			ar[i] = ar[i-1]+arr[i];
		}
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int ans = 0;
		for (int i = 0; i < ar.length; i++) {
			if(ar[i]>n) {
				ans = i-1;
				break;
			}
		}
		System.out.println(ans);
		sc.close();
		
	}

}
