acm CodeForces 492A

Description

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.

Sample Input

Input

1

Output

1

Input

25

Output

4

Sample Output

1 2 2 3

 

Hint

Illustration to the second sample: 

#include
#include
int const maxn=10001;
int a[maxn];
using namespace std;
int main()
{
    int n,sum;
    while(cin>>n)
    {
        int sum=0;
        a[1]=1;
        for(int i=2;i<=n;i++)
           a[i]=a[i-1]+i;
        for(int i=1;i<=n;i++)
            {
                sum+=a[i];
                if(sum==n)
                  {

                   cout<n)

                  {
                      cout<