Most people probably know the game rock-paper-scissors where two players count down and simultaneously form either a rock (fist), a pair of scissors (two outstretched fingers) or a piece of paper (outstretched hand) with their hands. Rock beats scissors, scissors beat paper and paper beats rock. If both players make the same choice, the game ends in a draw.

Sam Kass and Karen Bryla invented an extension of the classic selection game, and called it rock-paper-scissors-lizard-Spock. It operates on the same basic principle, but includes two additional weapons: the lizard (formed by the hand as a sock-puppet-like mouth) and Spock (formed by the Vulcan salute1 from the Star Trek series). This reduces the chances of a round ending in a tie (from 1/3 to 1/5). The game was mentioned in four episodes of television series The Big Bang Theory2.

In the game rock-paper-scissors-lizard-Spock each player picks a hand-shape, then both players reveal their choices at the same time. The winner is the one who defeats the other. The rules of rock-paper-scissors-lizard-Spock are:

• scissors cut paper

• paper covers rock

• rock crushes lizard

• lizard poisons Spock

• spock smashes scissors

• scissors decapitate lizard

• lizard eats paper

• paper disproves Spock

• Spock vaporizes rock

• rock crushes scissors

There are fifteen possible pairings of the five gestures. Each gesture beats two of the other gestures and is beaten by the remaining two. In a tie, the process is repeated until a winner is found. The original rules (rock beats scissors, scissors beats paper, paper beats rock) remain the same in the extended version of the game.

### Input

The input consists of two lines that each contain the name of a hand gesture that is respectively shown by player1 and player2 in a game of rock-paper-scissors-lizard-Spock: paper, rock, lizard, Spock or scissors.

### Output

The output consists of a single line that indicates which player wins the game. This line must contain one of the following descriptions:

• draw

• player1 wins

• player2 wins

Try to restrict the number of conditions that must be checked when deciding which player wins the game.

### Example

Input:

Spock
paper

Output:

player2 wins