Pay attention to the output section below, where you will see the information about flushing the output. Bearland is a grid with h rows and w columns. Rows are numbered 1 through h from top to bottom. Columns are numbered 1 through w from left to right. Every cell is either allowed (denoted by ' . ' in the input) or permanently blocked (denoted by ' # '). Bearland is a cold land, where heavy snow often makes travelling harder. Every day a few allowed cells are temporarily blocked by snow. Note, that this block works only on this particular day and next day any of these cells might be allowed again (unless there is another temporarily block). It's possible to move directly between two cells only if they share a side and none of them is permanently or temporarily blocked. Limak is a little polar bear who lives in Bearland. His house is at the top left cell, while his school is at the bottom right cell. Every day Limak should first go from his house to the school and then return back to his house. Since he gets bored easily, he doesn't want to visit the same cell twice on one day, except for the cell with his house, where he starts and ends. If Limak can reach a school and return home avoiding revisiting cells, he calls a day interesting . There are q days you must process, one after another. For each of these days you should check if it's interesting and print " YES " or " NO " on a separate line. In order to be able to read the description of the next day you should print the answer for the previous one and flush the output. It's guaranteed that a day with no cells temporarily blocked by snow would be interesting. It's also guaranteed that cells with Limak's house and school are never blocked (neither permanently or temporarily). The first line of the input contains three integers h , w and q ( 2 ≤ h , w ≤ 1000 , 1 ≤ q ≤ 10 000 ) — the height and the width of the grid, and the number of days, respectively. Next h lines describe which cells are allowed and w