CF1681D Required Length

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?

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

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.

In the second example, the following sequence of operations achieves the goal: 1. multiply $ x $ by $ 2 $ , so $ x = 2 \cdot 2 = 4 $ ; 2. multiply $ x $ by $ 4 $ , so $ x = 4 \cdot 4 = 16 $ ; 3. multiply $ x $ by $ 6 $ , so $ x = 16 \cdot 6 = 96 $ ; 4. multiply $ x $ by $ 9 $ , so $ x = 96 \cdot 9 = 864 $ .