Required Length Codeforces Solution | Codeforces Problem Solution 2022

Required Length Codeforces Solution | Codeforces Problem Solution 2022

D. Required Length

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

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

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

You want to make the length of decimal representation

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of x$x$ (without leading zeroes) equal to n$n$. What is the minimum number of operations required to do that?

Input

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

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Output

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