# #P1584C. Two Arrays

ID: 7475 Type: RemoteJudge 1000ms 256MiB Tried: 2 Accepted: 1 Difficulty: 3 Uploaded By: Tags>greedymathsortings*900

# Two Arrays

## Description

You are given two arrays of integers \$a_1, a_2, \ldots, a_n\$ and \$b_1, b_2, \ldots, b_n\$.

Let's define a transformation of the array \$a\$:

1. Choose any non-negative integer \$k\$ such that \$0 \le k \le n\$.
2. Choose \$k\$ distinct array indices \$1 \le i_1 < i_2 < \ldots < i_k \le n\$.
3. Add \$1\$ to each of \$a_{i_1}, a_{i_2}, \ldots, a_{i_k}\$, all other elements of array \$a\$ remain unchanged.
4. Permute the elements of array \$a\$ in any order.

Is it possible to perform some transformation of the array \$a\$ exactly once, so that the resulting array is equal to \$b\$?

The first line contains a single integer \$t\$ (\$1 \le t \le 100\$) — the number of test cases. Descriptions of test cases follow.

The first line of each test case contains a single integer \$n\$ (\$1 \le n \le 100\$) — the size of arrays \$a\$ and \$b\$.

The second line of each test case contains \$n\$ integers \$a_1, a_2, \ldots, a_n\$ (\$-100 \le a_i \le 100\$).

The third line of each test case contains \$n\$ integers \$b_1, b_2, \ldots, b_n\$ (\$-100 \le b_i \le 100\$).

For each test case, print "YES" (without quotes) if it is possible to perform a transformation of the array \$a\$, so that the resulting array is equal to \$b\$. Print "NO" (without quotes) otherwise.

You can print each letter in any case (upper or lower).

## Input

The first line contains a single integer \$t\$ (\$1 \le t \le 100\$) — the number of test cases. Descriptions of test cases follow.

The first line of each test case contains a single integer \$n\$ (\$1 \le n \le 100\$) — the size of arrays \$a\$ and \$b\$.

The second line of each test case contains \$n\$ integers \$a_1, a_2, \ldots, a_n\$ (\$-100 \le a_i \le 100\$).

The third line of each test case contains \$n\$ integers \$b_1, b_2, \ldots, b_n\$ (\$-100 \le b_i \le 100\$).

## Output

For each test case, print "YES" (without quotes) if it is possible to perform a transformation of the array \$a\$, so that the resulting array is equal to \$b\$. Print "NO" (without quotes) otherwise.

You can print each letter in any case (upper or lower).

## Samples

``````3
3
-1 1 0
0 0 2
1
0
2
5
1 2 3 4 5
1 2 3 4 5
``````
``````YES
NO
YES
``````

## Note

In the first test case, we can make the following transformation:

• Choose \$k = 2\$.
• Choose \$i_1 = 1\$, \$i_2 = 2\$.
• Add \$1\$ to \$a_1\$ and \$a_2\$. The resulting array is \$[0, 2, 0]\$.
• Swap the elements on the second and third positions.

In the second test case there is no suitable transformation.

In the third test case we choose \$k = 0\$ and do not change the order of elements.