D. An Alternative Way

time limit per test: 2 seconds

memory limit per test: 256 megabytes

input: standard input

output: standard output

You are given two arrays a and b, each of length n. You are allowed to perform the following operation on array a any number of times (including zero):

1. Choose two indices l and r such that 1 \le l \le r \le n;
2. For each index i from l to r (both inclusive),
   • Set a_i := a_i - 1 if i - l is odd.
   • Set a_i := a_i + 1 if i - l is even.

Determine whether you can make the array a equal to the array b by performing the operation any number of times.

Input

The first line contains a single integer t (1 \le t \le 10^4) — the number of test cases. Description of each test case follows.

The first line of each test case contains a single integer n (1 \le n \le 2\cdot10^5) — the length of the arrays a and b.

The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le 10^9) — the elements of the array a.

The third line of each test case contains n integers b_1, b_2, \ldots, b_n (1 \le b_i \le 10^9) — the elements of the array b.

It is guaranteed that the sum of n over all test cases does not exceed 2\cdot10^5.

Output

For each test case, print "YES" if you can make array a equal to array b and "NO" otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Example

Input

7
3
1 2 3
1 2 3
4
1 4 5 2
1 5 4 3
1
9
8
6
6 7 6 7 6 7
7 6 7 6 7 6
9
9 8 7 6 5 4 3 2 1
9 9 8 2 4 4 3 5 3
3
1 1 2
2 1 1
2
1 2
1 1

Output

YES
YES
NO
YES
NO
YES
NO

Note

For the first test case, arrays a and b are already equal.

For the second test case, let us choose l = 2 and r = 4. Now, we update the array a in the following manner:

• For i = 2, we have i - l = 2 - 2 = 0, which is even. Hence, set a_2 := a_2 + 1 = 4 + 1 = 5.
• For i = 3, we have i - l = 3 - 2 = 1, which is odd. Hence, set a_3 := a_3 - 1 = 5 - 1 = 4.
• For i = 4, we have i - l = 4 - 2 = 2, which is even. Hence, set a_4 := a_4 + 1 = 2 + 1 = 3.

Finally, we have array a = [1, 5, 4, 3] and array b = [1, 5, 4, 3].

For the third test case, it can be shown that it is impossible to make array a equal to array b.