Description

A number (with non-zero first digit) that reads the same from left to right and right to left is called a palindrome. For example, given a decimal number $56$, adding $56$ and $65$ (reading $56$ from right to left) gives $121$, which is a palindrome. Another example, for decimal number $87$:
STEP1: $87＋78= 165$
STEP2: $165＋561= 726$
STEP3: $726＋627＝1353$
STEP4: $1353+3531=4884$
Here, a step means performing one addition in base $N$. In the above example, it took at least $4$ steps to get the palindrome $4884$.
Write a program that, given a number $M$ in base $N$ ($2 ＜ N \le 10$ or $N=16$), finds the minimum number of steps needed to obtain a palindrome. If it's impossible to get a palindrome within $30$ steps (inclusive), output "Impossible".

Input Format

The first line contains a number $N$ ($2＜ N≤10$ or $N=16$) representing the base;
The second line contains a number $M$ in base $N$.

Output Format

The minimum number of steps needed. If it's impossible to get a palindrome within $30$ steps (inclusive), output "Impossible".

Sample

9
87

6