Problem O
Who Wins

You are at the casino playing a simplified game of Blackjack. The dealer has revealed their final hand. Your task is to determine who wins the round.

Blackjack is played with standard playing cards. Each card has a rank: 2-10, J, Q, K, or A. The value of each card is:

• Number cards 2-10 are worth their numeric value.

• Face cards J, Q, K are worth $10$.

• An A (Ace) is worth either $1$ or $11$, whichever is more favourable without causing the hand to exceed $21$.

The value of a hand is the maximum possible total not exceeding $21$. If all possible totals exceed $21$, the hand is said to be bust.

The outcome of the round is determined as follows:

• If both player and dealer bust, the result is a Push.

• If only the player busts, the Dealer wins.

• If only the dealer busts, the Player wins.

• Otherwise, the hand with the higher total wins.

• If both totals are equal, the result is a Push.

You are given both hands after all cards have been drawn. Determine the result.

Input

The first line contains an integer $d$ ($1 \le d \le 3$), the number of cards in the dealer’s hand. The second line contains $d$ strings describing the dealer’s cards. The third line contains an integer $p$ ($1 \le p \le 3$), the number of cards in the player’s hand. The fourth line contains $p$ strings describing the player’s cards.

Each card is one of: {2,3,4,5,6,7,8,9,10,J,Q,K,A}.

Output

Output exactly one of the following strings:

• Player if the player wins,

• Dealer if the dealer wins,

• Push if both player and dealer bust or both totals are equal.

3
J Q K
2
10 9

Player

2
10 9
3
J Q K

Dealer

3
8 9 10
3
J Q K

Push

3
5 6 7
3
5 6 7

Push

3
10 A 9
3
5 6 7

Dealer

3
5 6 7
3
10 A 9

Player

3
A A A
2
A A

Dealer