Problem C

Mia is a dice game for two players. Each roll consist of two dice. Mia involves bluffing about what a player has rolled, but in this problem we focus only on its scoring rules. Unlike most other dice games, the score of a roll is not simply the sum of the dice.

Instead, a roll is scored as follows:

  • Mia ($12$ or $21$) is always highest.

  • Next come doubles ($11$, $22$, and so on). Ties are broken by value, with $66$ being highest.

  • All remaining rolls are sorted such that the highest number comes first, which results in a two-digit number. The value of the roll is the value of that number, e.g. $3$ and $4$ becomes $43$.


The input will contain multiple, distinct test cases. Each test case contains on a single line four integers $s_0 \ s_1 \ r_0 \ r_1$ where $s_0 \ s_1$ represent the dice rolled by player $1$ and $r_0 \ r_1$ represents the dice rolled by player $2$. The input will be terminated by a line containing $4$ zeros.


For each test case, output which player won, or whether there was a tie, using exactly the format shown below.

Sample Input 1 Sample Output 1
1 2 1 3
3 3 2 1
6 6 4 4
6 5 1 1
4 2 2 4
0 0 0 0
Player 1 wins.
Player 2 wins.
Player 1 wins.
Player 2 wins.

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