Problem Statement

There is a sequence of length $N$: $a = (a_1, a_2, ..., a_N)$. Here, each $a_i$ is a non-negative integer.

Snuke can repeatedly perform the following operation:

• Let the XOR of all the elements in $a$ be $x$. Select an integer $i$ ($1 ≤ i ≤ N$) and replace $a_i$ with $x$.

Snuke's objective is to match $a$ with another sequence $b = (b_1, b_2, ..., b_N)$. Here, each $b_i$ is a non-negative integer.

Determine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive.

Constraints

• $2 ≤ N ≤ 10^5$
• $a_i$ and $b_i$ are integers.
• $0 ≤ a_i, b_i < 2^{30}$

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N
b_1 b_2 ... b_N

Output

If the objective is achievable, print the minimum necessary number of operations. Otherwise, print -1 instead.