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).