You are given two boards $a$ and $b$, each board has $1$ row and $n$ columns. Each cell in both boards can either be a digit from $0$ to $9$ or an empty cell represented by a dot character ..

You can perform the following operations on board $a$ zero or more times:

• Move an odd digit $(1, 3, 5, 7, 9)$ one cell to the left if that cell is empty. For example, if $a$ = 2..3, you can make it 2.3..
• Move an even digit $(0, 2, 4, 6, 8)$ one cell to the right if that cell is empty. For example, if $a$ = 2..3, you can make it .2.3.

Your task is to check if the board $a$ can be converted to the board $b$ after applying as many operations as needed.

The first line of the input contains a single integer $T$ ($1 \le T \le 250$), the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$), the number of columns of boards $a$ and $b$.

The next two lines contain the boards $a$ and $b$ respectively. Each board is represented by a string of length $n$ consisting of digits and dots.

The total sum of $n$ over all test cases doesn't exceed $2 \times 10^6$.

For each test case, print a single line with yes if board $a$ can be converted to board $b$. Otherwise, print no. The output is case insensitive.