N. A-to-B-Kedavra
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

At Obada's party, Anas asked Abode to teach him some magic spells, so he taught him the well-known "A-to-B-Kedavra" spell, which is used to exchange elements between arrays. Because Anas is new to the magic world, he couldn't perfectly cast it. Anas has two arrays $$$a$$$ and $$$b$$$ of length $$$n$$$. He can use the spell as follows:

  • Anas chooses an integer $$$i \: (1 \leq i \leq n)$$$ and a positive even integer $$$X \: (2 \leq X \leq a_i)$$$ and sets $$$a_i=a_i-X$$$.
  • He chooses an integer $$$j \: (1 \leq j \leq n)$$$ and sets $$$b_j=b_j+\frac{X}{2}$$$.

To test Anas's skills, Abode gave him a third array $$$c$$$ of length $$$n$$$ and asked him whether he could cast multiple (possibly zero) spells to make all three arrays equal ($$$a=b=c$$$). Can you help Anas??

Input

The first line contains a single integer $$$tc :\ (1 \leq tc \leq 100)$$$ — the number of testcases.

The first line of each testcase contains a single integer $$$n \: (1 \leq n \leq 2 \cdot 10^5)$$$.

The second line of each testcase consists of $$$n$$$ integers $$$a_i \: (1 \leq a_i \leq 10^9)$$$.

The third line of each testcase consists of $$$n$$$ integers $$$b_i \: (1 \leq b_i \leq 10^9)$$$.

The fourth line of each testcase consists of $$$n$$$ integers $$$c_i \: (1 \leq c_i \leq 10^9)$$$.

It is guaranteed that the sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each testcase print "YES" if Anas could pass Abode's test, and "NO" otherwise.

Example
Input
3
3
2 6 4
2 3 4
2 4 4
3
2 5 4
2 3 4
2 4 4
3
2 6 4
2 4 3
2 4 4
Output
YES
NO
YES
Note

In the first test case, Anas could choose $$$i=2$$$, $$$X=2$$$, and $$$j=2$$$.