Problem Statement

We have a grid with $H$ rows from top to bottom and $W$ columns from left and right. Initially, the square at the $i$-th row from the top and $j$-th column from the left has a lowercase English letter $A_{i,j}$.

Let us perform $Q$ operations on this grid. In the $i$-th operation, we are given integers $a_i$ and $b_i$ such that $1\leq a_i \leq H-1$ and $1\leq b_i\leq W-1$, and do the following.

• Let $R_1$, $R_2$, $R_3$, and $R_4$ be rectangular regions within the grid defined as follows:
• $R_1$ is the intersection of the top $a_i$ rows and leftmost $b_i$ columns;
  • $R_2$ is the intersection of the top $a_i$ rows and rightmost $W-b_i$ columns;
  • $R_3$ is the intersection of the bottom $H-a_i$ rows and leftmost $b_i$ columns;
  • $R_4$ is the intersection of the bottom $H-a_i$ rows and rightmost $W-b_i$ columns.
• Rotate $180$ degrees each of $R_1$, $R_2$, $R_3$, and $R_4$.

Here, a $180$-degree rotation of a rectangular region $R$ within the grid moves the character on the square at the $i$-th from the top and $j$-th column from the left in $R$ to the square at the $i$-th from the bottom and $j$-th column from the right in $R$. See also the figures for the samples.

Print the grid after all $Q$ operations.

Constraints

• $2\leq H, W$, and $HW \leq 5\times 10^5$.
• $A_{i,j}$ is a lowercase English letter.
• $1\leq Q\leq 2\times 10^5$
• $1\leq a_i\leq H - 1$
• $1\leq b_i\leq W - 1$

Input

The input is given from Standard Input in the following format:

H W
A_{1,1}\cdots A_{1, W}
\vdots
A_{H,1}\cdots A_{H, W}
Q
a_1 b_1
\vdots
a_Q b_Q

Output

Print the grid after the operations in the following format, where $B_{i,j}$ is the character on the square $(i,j)$ on the final grid.

B_{1,1}\cdots B_{1, W}
\vdots
B_{H,1}\cdots B_{H, W}