JOI Logo Design

Chairman K has decided to design a logo for merchandise supporting the Japanese Olympiad in Informatics contestants. One day Chairman K hit on the idea of arranging the characters 'J', 'O', and 'I' in a circle as the logo. The idea carries a wish for people to enjoy JOI.

For an integer $k \ge 0$, a level $k$ JOI sequence is defined as follows.

• A level 0 JOI sequence is a string of length 1 consisting of one of the characters 'J', 'O', and 'I'.
• A level $k+1$ JOI sequence is a string of length $4^{k+1}$ whose first $4^k$ characters are all 'J', whose next $4^k$ characters are all 'O', whose next $4^k$ characters are all 'I', and whose last $4^k$ characters form a level $k$ JOI sequence.

Chairman K now has a sheet of paper with $4^K$ characters written in a circle. Each character on the paper is one of 'J', 'O', and 'I'. Chairman K will rewrite some of the characters so that, when the characters on the paper are read clockwise around the circle starting from some character, they form a level $K$ JOI sequence. He wants to keep the number of rewritten characters as small as possible.

Given a string of length $4^K$ written in a circle on the paper, write a program that finds the minimum number of characters that must be rewritten so that reading the string clockwise around the circle from some starting character yields a level $K$ JOI sequence.

Read the following data from standard input.

• The first line contains an integer $K$. This means that $4^K$ characters are written in a circle on the paper.
• The second line contains a string of length $4^K$ consisting of 'J', 'O', and 'I'. This means that reading the characters on the paper clockwise around the circle starting from some character yields this string.

Print the minimum number of characters Chairman K rewrites on a single line to standard output.

• $1 \le K \le 10$.