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

\(1\le n \le 10^{5}\)

\(0\leq r_i \leq 10^6\)

\(0\leq c_i \leq 10^6\)

\(1\le q \le 10^{5}\)

\(1 \leq r_1, c_1 \leq n\)

\(1 \leq r_2, c_2 \leq n\)