This is a run-twice (communication) problem. At the Fairy Warehouse, Nygglatho prepared an unusual game for Chtholly and Willem. They would be separated and unable to exchange a single word. Between them there would be only a black-and-white picture — one that Nygglatho could shift, rotate, reflect, or even invert its colors. Nygglatho saw it as a test of how well they understood each other. Chtholly and Willem perhaps saw only another kind of promise. No matter how the world turned, they would still find the same place. The two players are Chtholly and Willem. The jury, acting as Nygglatho, first communicates with Chtholly. After Chtholly finishes, the jury communicates with Willem. Chtholly and Willem may agree on the strategy they will use beforehand, but they cannot directly pass information to each other. In each test case, Nygglatho prepares a black-and-white picture consisting of (n \times n) cells and chooses a target cell (x). The rows and columns are numbered from (1) to (n). The picture contains (w) black cells. It is guaranteed that (\gcd(n,w)=1). Nygglatho first shows the picture and the target cell (x) to Chtholly. Chtholly must choose two cells and swap their colors. The two cells are allowed to be the same. If they are the same, or if they have the same color, the picture does not change. She cannot send Willem any other information. Swapping colors does not move the target cell. Nygglatho then secretly transforms the picture. She may perform the following operations any number of times, possibly zero, in any order: Choose two integers (d_r) and (d_c) ((0\le d_r,d_c \lt n)) and cyclically shifts the picture. Every cell ((r,c)) moves to (\left(\left(r-1+d_r\right)\bmod n+1,\left(c-1+d_c\right)\bmod n+1\right)); Rotate the picture clockwise by (90^\circ). One such rotation moves every cell ((r,c)) to ((c,n+1-r)); Reflect the picture across its vertical axis. Such a reflection moves e