Two Triangles

The first line has $1$ number, the second line has $2$ numbers, and so on, up to line $N$ with $N$ numbers. Triangles $A$ and $B$ are arranged as shown in the figure below. Each position holds $0$ or $1$.

You can rotate the triangle $120^◦$ clockwise or counterclockwise, or reflect it left to right.

For example, rotating triangle $A$ gives the triangles below.

Reflecting $A$ gives the triangle below.

The difference between two triangles is the number of positions where their values differ when the two triangles are overlapped.

For example, when $A$ and $B$ are overlapped, the values differ at the leftmost position of row 2 and at the leftmost and rightmost positions of row 3. So the difference between $A$ and $B$ is $3$. However, if $A$ is rotated $120^◦$ counterclockwise (the right triangle in the second figure) and overlapped with $B$, only the second position from the left in row 3 differs. So that difference is $1$.

You are given triangles $A$ and $B$. You can rotate and reflect $A$ as many times as you want, or not at all. There is no limit on the number of rotations or reflections.

Rotate or reflect $A$ to make its difference from $B$ as small as possible. Find that minimum difference.

The first line contains the size $N$ of $A$ and $B$.

Lines 2 through $N + 1$ give the values at each position of $A$. Line $i + 1$ ($1 ≤ i ≤ N$) contains the $i$ integers in row $i$ of $A$, separated by spaces, from left to right.

Lines $N + 2$ through $2N + 1$ give the values at each position of $B$. Line $i + N + 1$ ($1 ≤ i ≤ N$) contains the $i$ integers in row $i$ of $B$, separated by spaces, from left to right.

Print the minimum difference from $B$ among all triangles you can get by rotating and reflecting $A$.

• All given numbers are integers.
• $1 ≤ N ≤ 10$
• Each value in $A$ and $B$ is $0$ or $1$.