408890: GYM103372 E Flowerbed Redecoration

E. Flowerbed Redecorationtime limit per test1 secondmemory limit per test1024 megabytesinputstandard inputoutputstandard output

Joon-Pyo decorated a flowerbed in front of his home. The flowerbed is in the shape of an $$$n \times m$$$ grid, and one flower is planted in each cell. There are 26 colors, one corresponding to each uppercase letter from A to Z. Suddenly, he wanted to redecorate the flowerbed.

The flowerbed is too large to adjust the flowers one by one. He rented some equipment that can lift and rotate a square plot of land with a side length of $$$d$$$. He planned the construction in the following order, expecting the flowerbed to be properly redecorated.

1. Place the equipment so that exactly the flowers in the first $$$d$$$ rows and the first $$$d$$$ columns are inside.
2. Rotate the $$$d \times d$$$ square inside the equipment $$$90^\circ$$$ clockwise. If this square contains flowers from the last $$$d$$$ rows and the last $$$d$$$ columns, then the construction is finished. Otherwise, if this square does not contain flowers in the last $$$d$$$ columns, move the equipment $$$x$$$ squares to the right. Otherwise, move the equipment down by $$$y$$$ squares and all the way to the left so it contains flowers from the first $$$d$$$ columns.
3. Repeat step 2 until construction is finished.

Note that the equipment will never go out of the flowerbed, as $$$x$$$, $$$y$$$, and $$$d$$$ are carefully determined before construction begins.

He cannot start construction without knowing the outcome. Write a program that outputs the result.

Input

On the first line, five integers $$$n$$$, $$$m$$$, $$$y$$$, $$$x$$$, and $$$d$$$ are given. ($$$1 \leq n \times m \leq 10^6 $$$, $$$ 1 \leq y \leq n$$$, $$$ 1 \leq x \leq m $$$, $$$ 1 \leq d \leq \min(n, m)$$$, $$$\boldsymbol{n \equiv d \pmod y}$$$, $$$\boldsymbol{m \equiv d \pmod x}$$$).

Each of the next $$$n$$$ lines contains exactly $$$m$$$ uppercase letters, the current flowerbed.

Output

Output $$$n$$$ lines, each containing $$$m$$$ uppercase letters, the flowerbed after the planned construction.

ExamplesInput

4 4 1 1 2
AAAA
BBBB
AAAA
BBBB

Output

BAAA
ABBB
BAAA
BBBA

Input

6 5 1 2 3
RBRCY
YBPBR
PBRCY
CYPBR
PBRCY
CYPBR

Output

PYRBR
CRCBB
PPBPY
CRCYB
YRBCY
PYRBR