There are $N+2$ cells arranged in a row. Let cell $i$ denote the $i$-th cell from the left.

There is one stone placed in each of the cells from cell $1$ to cell $N$.
For each $1 \leq i \leq N$, the stone in cell $i$ is white if $S_i$ is W, and black if $S_i$ is B.
Cells $N+1$ and $N+2$ are empty.

You can perform the following operation any number of times (possibly zero):

• Choose a pair of adjacent cells that both contain stones, and move these two stones to the empty two cells while preserving their order.
  More precisely, choose an integer $x$ such that $1 \leq x \leq N+1$ and both cells $x$ and $x+1$ contain stones. Let $k$ and $k+1$ be the empty two cells. Move the stones from cells $x$ and $x+1$ to cells $k$ and $k+1$, respectively.

Determine if it is possible to achieve the following state, and if so, find the minimum number of operations required:

• Each of the cells from cell $1$ to cell $N$ contains one stone, and for each $1 \leq i \leq N$, the stone in cell $i$ is white if $T_i$ is W, and black if $T_i$ is B.

If it is possible to achieve the desired state, print the minimum number of operations required. If it is impossible, print -1.

• $2 \leq N \leq 14$
• $N$ is an integer.
• Each of $S$ and $T$ is a string of length $N$ consisting of B and W.

Using . to represent an empty cell, the desired state can be achieved in four operations as follows, which is the minimum:

• BWBWBW..
• BW..BWBW
• BWWBB..W
• ..WBBBWW
• WWWBBB..