def solution$($M$,$ N$)$: # Convert the number of $1$x$1$ and $2$x$2$ tiles into the equivalent number of $1$x$1$ tiles total$\_$tiles $=$ M $+4*$ N # The side of the largest square that can be created is the square root of the total number of $1$x$1$ tiles max$\_$side $=$ int$($total$\_$tiles $**0\mathrm{.}5)$ # Start from the max possible side and decrease until you find the largest possible square for side in range$($max$\_$side, $0,-1)$: # Calculate how many $2$x$2$ and $1$x$1$ tiles would be needed for this side length required$\_2$x$2=($side $//2)**2$ required$\_1$x$1=($side $\%2)*$ side # Check if we have enough $2$x$2$ tiles and if the remaining $1$x$1$ tiles can cover the rest if N $>=$ required$\_2$x$2$ and M $>=$ required$\_1$x$1$: return side # If not enough $2$x$2$ tiles, see if we can make up the difference with $1$x$1$ tiles if N $<$ required$\_2$x$2$: # Calculate the deficit of $1$x$1$ tiles after using all $2$x$2$ tiles needed$\_1$x$1=4*($required$\_2$x$2-$ N$)$ # Check if we have enough $1$x$1$ tiles after covering the required $1$x$1$ area if M $+4*$ N $>=$ needed$\_1$x$1+$ required$\_1$x$1$: return side # If no square can be created, return $0$ return $0$