E. Even Even Odd Odd
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Lunchbox has two arrays $$$a_1, a_2, \ldots, a_n$$$ and $$$b_1, b_2, \ldots, b_n$$$, each of length $$$n$$$. It is guaranteed that $$$a_i \leq b_i$$$ for each $$$1 \leq i \leq n$$$.

He is allowed to perform either of the following two operations in any order, as many times as he wants (possibly zero):

  • If there are an even number of even elements in $$$a$$$, add a positive even number to any element in $$$a$$$.
  • If there are an odd number of odd elements in $$$a$$$, add a positive odd number to any element in $$$a$$$.

Is it possible to turn $$$a$$$ into $$$b$$$?

Input

Input consists of multiple tests. The first line contains $$$t$$$, the number of tests ($$$1 \leq t \leq 10^5$$$).

The first line of each test contains $$$n$$$, the length of the arrays ($$$1 \leq n \leq 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$).

The third line contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \leq b_i \leq 10^9$$$).

It is guaranteed that the sum of $$$n$$$ across all tests does not exceed $$$10^5$$$.

Output

For each test, output YES or NO.

Example
Input
7
3
1 3 5
1 3 6
3
1 3 5
1 3 7
2
1 1
1 1
1
2
1000000000
5
1 2 3 4 5
6 7 8 9 10
5
1 1 1 1 1
3 3 3 3 4
2
1 2
1 4
Output
YES
YES
YES
NO
NO
YES
NO
Note

In the first test, since there are initially $$$3$$$ odd elements in $$$a$$$, we are allowed to add $$$1$$$ (an odd integer) to $$$a_3$$$. After this operation, $$$a = [1, 3, 6] = b$$$.

In the second test, since there initially $$$0$$$ even elements in $$$a$$$, we are allowed to add $$$2$$$ (an even integer) to $$$a_3$$$. After this operation, $$$a = [1, 3, 7] = b$$$.

In the third test, it may be possible that $$$a=b$$$ without doing any operations.

In the fourth test, there are initially $$$0$$$ odd elements and $$$1$$$ even element, so we cannot perform any operations.