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Statement

The XOR operation is a very common operation in computers. For a binary number with only one digit, the XOR operation output is true (1) if and only if the two input values are different, otherwise the output is false (0), that is, ''the same is 0, different is 1".

For some numbers, we have a bitwise exclusive OR operator denoted as $a_{(10)}\oplus b_{(10)}$, which means converting $a,b$ into binary bits and performing an exclusive OR operation on each bit to get a new number. For example, $5\oplus9$ is calculated as follows:

so we can calculate $5\oplus9=12$. In mainstream programming languages, the exclusive OR symbol is generally ^ . For example, in C++, typing int x = a ^ b; means $x\leftarrow a\oplus b$.

In this problem, you are given an array $a$ of length $n$. For each index $i$ in the array that satisfies $0 \le i < n-1$, you can perform the following operation at most once^[1]:

• The assignment is $a_i := a_i \oplus a_{i+1}$, where $\oplus$ represents the bitwise exclusive OR operation. It should be noted that $a_i$ represents the $i+1$th number in the array $a$, for example, $a_0=1$ in the array $[1,2,3,4,5]$ instead of the $i$ base.

You can choose the indices and perform the operations in any order. Given another array $b$ of length $n$, determine whether $a$ can be transformed into $b$ using the operations.

Input

The first line contains an integer $n$ ($2 \le n \le 2 \cdot 10^5$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i < 2^{30}$).

The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($0 \le b_i < 2^{30}$).

Output

For each test case, if $a$ can be converted to $b$, then output ''Yes'' (without quotes); otherwise, output "No''.

Samples

5
1 2 3 4 5
3 2 7 1 5

Yes

3
0 0 1
1 0 1

No

3
0 0 1
0 0 0

No

4
0 0 1 2
1 3 3 2

No

 6
 1 1 4 5 1 4
 0 5 4 5 5 4

Yes

Notes

In the first example, you can perform the following operations in the following order:

1. Choose subscript $i=2$ so that $a_2 := a_2 \oplus a_3 = 7$, and $a$ becomes $[1, 2, 7, 4, 5]$;
2. Choose subscript $i=3$ so that $a_3 := a_3 \oplus a_4 = 1$, and $a$ becomes $[1, 2, 7, 1, 5]$;
3. Choose subscript $i=0$ so that $a_0 := a_0 \oplus a_1 = 3$, and $a$ becomes $[3, 2, 7, 1, 5]$.

From this we can see that $a$ can be transformed into $b$.