Quadtree Image Compression

Compute the output length of the quadtree image compression scheme. The image is an $L \times L$ square of $L^2$ pixels, and every pixel is either a $0$-pixel or a $1$-pixel.

The scheme works like this.

1. If the image contains both $0$-pixels and $1$-pixels, write a single $1$ to record that the image is split into $4$ sub-images by rule 2. If the image contains only one kind of pixel, write $00$ when every pixel is $0$ and $01$ when every pixel is $1$, then stop.
2. Split image $I$ into $4$ sub-images $A$, $B$, $C$, $D$ of equal size as shown below. Then apply rule 1 to each sub-image in the order $A$, $B$, $C$, $D$.

The length of the compressed image is the number of bits in its encoding. $L$ is a power of $2$ and $1 \le L \le 64$.

The first line contains the integer $L$. Each of the next $L$ lines contains $L$ bits, with a single blank between two adjacent bits. Every bit is $0$ or $1$.

Print the length of the compressed image, that is, the number of bits, on one line.