You're given an array $$$a$$$ of length $$$n$$$. For each index $$$i$$$ such that $$$1 \le i \lt n$$$, you can perform the following operation at most once:

Assign $$$a_i := a_i \oplus a_{i+1}$$$, where $$$\oplus$$$ denotes the bitwise XOR operation. .

You can choose indices and perform the operations in any sequential order.

Given another array $$$b$$$ of length $$$n$$$, determine if it is possible to transform $$$a$$$ to $$$b$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).

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

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

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output "YES" (quotes excluded) if $$$a$$$ can be transformed to $$$b$$$; otherwise, output "NO". You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Note

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

Choose index $$$i=3$$$ and assign $$$a_3 := a_3 \oplus a_4 = 7$$$, and $$$a$$$ becomes $$$[1, 2, 7, 4, 5]$$$.
Choose index $$$i=4$$$ and assign $$$a_4 := a_4 \oplus a_5 = 1$$$, and $$$a$$$ becomes $$$[1, 2, 7, 1, 5]$$$.
Choose index $$$i=1$$$ and assign $$$a_1 := a_1 \oplus a_2 = 3$$$, and $$$a$$$ becomes $$$[3, 2, 7, 1, 5]$$$.

Adjacent XOR

Examples