Problem Statement

There is a tournament with $2^N$ participants, numbered $1$ to $2^N$.

The tournament proceeds as follows:

• First, each participant is given a red or blue hat. You are given the color of the hat for each participant as the string $S$. Specifically, participant $i$ is given a red hat if the $i$-th character ($1 \leq i \leq 2^N$) of $S$ is R, and a blue hat if it is B.
• Then, the following operation is repeated until there is only one participant remaining:
• Let $2k$ be the current number of participants. Divide the participants into $k$ pairs. You can freely choose how to pair them. Then, a match is held for each pair; the winner remains, and the loser leaves the tournament. The participants are numbered in descending order of strength, so the participant with the smaller number always wins.

A match between two participants wearing red hats is called a boring match. Your goal is to arrange the pairings so that no boring matches occur during the tournament.

Whether the goal is achievable or not depends on the string $S$. Hence, you have decided to tamper with $S$ before the start of the tournament. Specifically, you can perform the following operation zero or more times:

• Choose two adjacent characters in $S$ and swap them.

Determine whether it is possible to achieve the goal after operations. If it is, find the minimum number of operations required.

Constraints

• $1 \leq N \leq 18$
• $S$ is a string of length $2^N$ consisting of R and B.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
S

Output

If it is impossible to achieve the goal, print $-1$. Otherwise, print the minimum number of operations required.