Wizard Shark and Firestorm

Wizard Shark can cast Firestorm by combining Fireball and Tornado. Today he wants to practice Firestorm on an ice sheet divided into a grid of size $2^N \times 2^N$. Position $(r, c)$ means row $r$ and column $c$ of the grid, and $A[r][c]$ means the amount of ice at $(r, c)$. If $A[r][c]$ is 0, there is no ice there.

To cast Firestorm, he must decide on a level $L$ for each cast. Firestorm first divides the grid into subgrids of size $2^L \times 2^L$. Then it rotates every subgrid 90 degrees clockwise. After that, any cell that is not adjacent to at least 3 cells containing ice loses 1 from its amount of ice. The cells adjacent to $(r, c)$ are $(r-1, c)$, $(r+1, c)$, $(r, c-1)$, and $(r, c+1)$. The integers written in the cells of the figures below are just labels to distinguish the cells.

Before casting the spell	$L = 1$	$L = 2$

Wizard Shark wants to cast Firestorm $Q$ times in total. After casting all the Firestorms, find the following two values.

1. The sum of the remaining ice $A[r][c]$
2. The number of cells occupied by the largest chunk of remaining ice

If a cell containing ice is adjacent to another cell containing ice, the two cells are said to be connected. A chunk is a set of connected cells.

The first line gives $N$ and $Q$. From the second line, $2^N$ lines give the amount of ice in each cell of the grid. The integer given at position $c$ in the $r$-th line is $A[r][c]$.

The last line gives the levels $L_1, L_2, \dots, L_Q$ that Wizard Shark cast, in order.

Print the sum of the remaining ice $A[r][c]$ on the first line, and the number of cells occupied by the largest chunk on the second line. If there is no chunk, print 0.

• $2 \le N \le 6$
• $1 \le Q \le 1,000$
• $0 \le A[r][c] \le 100$
• $0 \le L_i \le N$