Required Length solution codeforces

You are given two integer numbers, $n$ and $x$ . You may perform several operations with the integer $x$ .

Each operation you perform is the following one: choose any digit $y$ that occurs in the decimal representation of $x$ at least once, and replace $x$ by $x \cdot y$ .

You want to make the length of decimal representation of $x$ (without leading zeroes) equal to $n$ . What is the minimum number of operations required to do that?

Input

The only line of the input contains two integers $n$ and $x$ ( $2 \leq n \leq 19$ ; $1 \leq x < 10^{n - 1}$ ).

Output

Print one integer — the minimum number of operations required to make the length of decimal representation of $x$ (without leading zeroes) equal to $n$ , or $- 1$ if it is impossible.

Examples

input

Copy

2 1

output

Copy

-1

input

Copy

3 2

output

Copy

input

Copy

13 42

output

Copy

Note

In the second example, the following sequence of operations achieves the goal:

multiply $x$ by $2$ , so $x = 2 \cdot 2 = 4$ ;
multiply $x$ by $4$ , so $x = 4 \cdot 4 = 16$ ;
multiply $x$ by $6$ , so $x = 16 \cdot 6 = 96$ ;
multiply $x$ by $9$ , so $x = 96 \cdot 9 = 864$ .

SOLUTION

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Required Length solution codeforces

SOLUTION

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