Goal
Your task is to find the correct starting order of a deck of cards so that, when the cards are dealt according to the procedure below, they appear in the requested pattern.
The Challenge
Arrange the cards in a deck so that, when they are dealt using the following procedure, they produce the given target pattern.
Repeat the following steps until the deck is empty:
1. Deal the top card.
2. Move the new top card to the bottom of the deck.
Card Notation
The following mapping is used for suits:
S = Spades
H = Hearts
D = Diamonds
C = Clubs
The following mapping is used for card values:
1 = Ace
7 = 7
8 = 8
9 = 9
0 = 10
J = Jack
Q = Queen
K = King
Each card is represented by a two-character string.
For example:
S1 = Ace of Spades
The cover image of this puzzle shows one valid solution.
Example
Consider the following starting deck, where the leftmost card represents the top of the deck:
C7CQH8SJD9
The following shows how the deck changes at each iteration:
Iteration 1
Dealt order so far: C7
Remaining deck: H8SJD9CQ
Iteration 2
Dealt order so far: C7H8
Remaining deck: D9CQSJ
Iteration 3
Dealt order so far: C7H8D9
Remaining deck: SJCQ
Iteration 4
Dealt order so far: C7H8D9SJ
Remaining deck: CQ
Iteration 5
Dealt order so far: C7H8D9SJCQ
Remaining deck: empty
Input
Line 1: N — An integer, the number of cards in the deck.
Line 2: D — A string, the desired dealing order of the N cards, separated by a space.
Output
Line 1: A string — the initial order of the deck of N cards, separated by a space, so that, when dealt according to the procedure, they produce the desired final order.
Constraints
1 ≤ N ≤ 200
This puzzle uses a non-standard deck: cards may be repeated, and only the specified ranks are used.
