log2

You are given a strictly positive integer $x$ written in base 16.

Task

Calculate the floor of the base-2 logarithm of $x$.
More formally, calculate $\lfloor log_{2}(x) \rfloor$.

Input

A strictly positive integer $x$ written in base 16.

Output

The natural number $\lfloor log_{2}(x) \rfloor$ written in base 10.

Restrictions

• $x$ has maximum $100\ 000$ digits in base 16;
• $x$ can contain leading zeros;
• The digits in base 16 are, in order, 0123456789ABCDEF.

Example 1

stdin

001

stdout

0

Example 2

stdin

4A

stdout

6

Explanation

In the first example, $\text{001}_{(16)}$ is $1_{(10)}$, so $\lfloor log_{2}(x) \rfloor = 0_{(10)}$.
In the second example, $\text{4A}_{(16)}$ is $74_{(10)}$, so $\lfloor log_{2}(x) \rfloor = 6_{(10)}$.