# Problem C

Card Hand Sorting

Sorting is done by moving one card at a time from its current position to a new position in the hand, at the start, end, or in between two adjacent cards. What is the smallest number of moves required to sort a given hand of cards?

## Input

The first line of input contains an integer $n$ ($1
\le n \le 52$), the number of cards in the hand. The
second line contains $n$
pairwise distinct space-separated cards, each represented by
two characters. The first character of a card represents the
rank and is either a digit from `2` to
`9` or one of the letters `T`, `J`, `Q`, `K`, and `A` representing Ten, Jack, Queen, King and Ace,
respectively, given here in increasing order. The second
character of a card is from the set {`s`, `h`, `d`, `c`} representing
the suits spades $\spadesuit
$, hearts $\heartsuit
$, diamonds $\diamondsuit $, and
clubs $\clubsuit
$.

## Output

Output the minimum number of card moves required to sort the hand as described above.

Sample Input 1 | Sample Output 1 |
---|---|

4 2h Th 8c Qh |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

7 9d As 2s Qd 2c Jd 8h |
2 |

Sample Input 3 | Sample Output 3 |
---|---|

4 2h 3h 9c 8c |
0 |