Fashion in card games is capricious. Just two years ago no one knew
anything about God forsaken planet Texas and game “rummy” which Texans
love so much. Today you’ll hardly find a casino in the Galaxy
where people don’t dice away their fortune at this simple game.
Galaxy Committee on card games set out the following rules for rummy. The
game is played with two decks of n cards, all the cards of different
kinds, numbered from one to n. In the beginning, each of the two players
takes a full deck and shuffles it thoroughly. The deck is laid on
the table face down. Then both players show their upper cards at the same
time. If the cards are of the same kind, both cards are put away and
aren’t used in the game anymore. In the other case the player whose card was
of a greater kind, takes both cards and puts them into the bottom of his
deck so that the greater card is at the very bottom and the minor is right atop of it.
Then the players show the upper cards of their decks again.
The player loses if he is out of cards. If the players are out of cards
at the same time, it’s a draw.
Card-sharper Dustin has recently put a tiny scanner in his eye, which lets
him see the order of the cards in the partner’s deck. Now he wants to
shuffle his cards in such a way that guarantees him a victory. Of course,
if Dustin puts his cards in the same order as his partner’s, he’ll easily
get the draw. But that’s not his cup of tea, because he only needs victory.
The first line contains an integer n (2 ≤ n ≤ 500) that is the
number of cards in each player’s deck. The second line contains a
permutation of numbers from 1 to n denoting kinds of cards in Dustin’s
partner’s deck in top-down order.
Output the word “YES” in the first line, if Dustin can shuffle his cards
in the order which provides him a victory. In the second line
output the sought order of cards in Dustin’s deck. If Dustin cannot
provide a victory, output a single word “NO”.
2 3 4 1
2 4 1 3
Problem Author: Andrey Demidov
Problem Source: Open Ural FU Personal Contest 2012