D. Required Lengthtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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?InputThe only line of the input contains two integers n and x (2 \le n \le 19; 1 \le x < 10^{n-1}).OutputPrint 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.ExamplesInput
2 1
Output
-1
Input
3 2
Output
4
Input
13 42
Output
12
NoteIn 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. 
2 1

-1 
['brute force', 'dfs and similar', 'dp', 'hashing', 'shortest paths', '*1700']