Alice and Bob are playing a board game. They have $n \times n$ boards and two arrays $a$ and $b$ of length $n$. The value of each cell in the $i^{th}$ row and $j^{th}$ row is $a[i]+b[j]$. Alice asks $q$ questions to Bob. In each question, Alice provides two cells $A$ and $B$. She asks the following questions to Bob:

Are there any paths from $A$ to $B$ that contains the same parity as $A$ and $B$.

Note: Bob can move from one cell to 8 neighbor cells in each step.

Input format

• First line: An integer $n$ denoting the length of arrays
• Second line: $n$ integers with $a_{i}$ representing array $a$
• Third line: $n$ integers with $b_{i}$ representing array $b$
• Fourth line: An integer $q$  denoting the number of test cases
• For each test case:
  • First line: Two integers $r_{1},c_{1}$ denoting the row and the column of $A$
  • Second line: Two integers $r_{2},c_{2}$denoting the row and the column of $B$

Output format

For each query, if there exists a path (for example, $C$) from $A$ to $B$ that contains the same parity as $A$ and $B$, then print YES. If the parity of A and B are different, then print NO.

Constraints

$1\le n \le 10^{5}$

$0\leq r_i \leq 10^6$

$0\leq c_i \leq 10^6$

$1\le q \le 10^{5}$

$1 \leq r_1, c_1 \leq n$

$1 \leq r_2, c_2 \leq n$