Sequence Conversion

You are given two arrays of non-negative integers $a\_1, a\_2, \dots, a\_N$ and $b\_1, b\_2, \dots, b\_N$.

You can perform the following operation several times:

• Choose a non-negative integer $x$ and an index $1 \leq i < N$. Then change $a\_i$ to $a\_i \oplus x$ and change $a\_{i+1}$ to $a\_{i+1} \oplus x$.

Expression $x \oplus y$ means bitwise xor of two numbers $x$ and $y$.
In binary representation, if the $i$-th digit of x and y is equal, then the $i$-th digit of $x \oplus y$ is $0$, and if not, it is $1$.
The given operation exists in all modern programming languages. For example, in C++ and Java, it is represented as $x\ ^{\wedge}\ y$.

You want to convert $\\{a\_i\\}$ to $\\{b\_i\\}$ by performing the minimum number of operations.

Find the minimum number of operations to convert $\\{a\_i\\}$ to $\\{b\_i\\}$.

If you cannot convert $\\{a\_i\\}$ to $\\{b\_i\\}$ with the given operation, print $-1$.

The first line contains an integer $N$, where $N$ denotes the length of the two sequences.

The second line contains $N$ space-separated non-negative integers $a\_1, a\_2, \dots, a\_N$.

The third line contains $N$ space-separated non-negative integers $b\_1, b\_2, \dots, b\_N$.

Print $-1$, if it is impossible to change the sequence $\\{a\_i\\}$ to $\\{b\_i\\}$.

Otherwise, print the minimum number of operations needed to change the sequence $\\{a\_i\\}$ to $\\{b\_i\\}$.

• $1 \leq N \leq 10^6$
• $0 \leq a\_i, b\_i < 2^{30}$ $(1 \le i \le N)$