Vanya and Cubes

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:

问题链接：https://vjudge.net/contest/276590#problem/B

问题分析：第一行有1个正方形，第二行要放1+2=3个，第三行要1+2+3=6个······以此类推，第i行要
1+2+3+4+···+（i-1）+1个，先要求输入总共有n个正方形，输出可以排成几行。

解决方案：定义一个数组a[100]用于存放每行所需的方格数，循环计算从数组第一个数开始算总和，算到当总和大于输入的n（有n个方块）时停止，输出此时求和求的数组下标，即为所需行数。注意如果求和总和sum>n,为i行；sum==n，则为i+1行。

#include 
using namespace std;

int main()
{
	int i, n,sum=0,k=2,s=99;
	int a[100];
	cin >> n;
	for(i=0;i n)cout << i ;break;
	}

}