Given two cyclic sequences A and B each of length n, consisting of 0 and 1. In cyclic sequence $a_{i+1}$ comes after $a_i$ and $a_0$ comes after $a_{n-1}$. In a single turn you can flip three consecutive elements: $a_i$, $a_{(i+1)\bmod n}$ and $a_{(i+2) \bmod n}$. Flipping element is altering its value: if it is 0, it becomes 1, and vice versa. What is the minimum number of turns you need to make to obtain sequence B from A?

Input format

First line of input contains single integer n ($3 \leq n \leq 2 \cdot 10^5$) — the length of A and B.

The second line of input contains n integers $a_i$ ($0 \leq a_i \leq 1$) — sequence A.

The third line of input contains n integers $b_i$ ($0 \leq b_i \leq 1$) — sequence B.

Output format

Print single integer — number of operations if it is possible to obtain B from A. Otherwise print "Impossible" (without quotes).