CF1584C.Two Arrays

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).

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.