### Problem Statement

"Step right up!" cries the barker. "Step up to play a simple game of arithmetic! Beat our man and we'll pay out five to two!"

You watch carnival patrons stepping up to try their hand at Fifteen. The game is played on a long, thin table divided into nine sections marked with the numerals 1 through 9. Behind the table stands a carnival worker, called the dealer, who makes the first move of the game. The dealer places a quarter (twenty-five cents) on a numeral of his choosing. Then the patron puts a dime (ten cents) on some other numeral. Then it is the dealer's turn again, and moves proceed in alternation. With each move, one may only choose a numeral that hasn't been covered yet. The object of the game is to use one's coins to cover three numerals that add up to 15. It doesn't matter if a player has covered more than three numerals, as long as exactly three of them sum to 15. The game ends as soon as such a sum is formed, or, at the latest, once every numeral has been covered. If the patron makes 15, he wins all the coins on the table. Otherwise, the dealer keeps the money.

You've been watching for a while, and the dealer almost always wins. Regardless of the five-to-two payout, the dealer has a tremendous advantage. Not only does he get the first move, but he can win by making 15 before the patron or merely by preventing the patron from making 15. Then again, if the dealer always won, the supply of patrons would quickly dry up. Sometimes the dealer makes a weak move that the patron can exploit to win the game.

Given a record of the moves made so far, the dealer having made the most recent move, determine whether the patron can win the game. The record is a int[] containing, in order of play, the numerals covered so far. The moves are guaranteed to be such that the game has not ended yet. If, regardless of the patron's next move, the dealer wins by playing optimally from this point on, return the String "LOSE" (quotes for clarity only). If there is a way for the patron to win regardless of the dealer's moves, return a String in the format "WIN X", where X is replaced by the numeral the patron should cover next in order to win. If several moves are equally promising, choose the one with the lowest numerical value.

### Definition

 Class: Fifteen Method: outcome Parameters: int[] Returns: String Method signature: String outcome(int[] moves) (be sure your method is public)

### Notes

-When returning a result of the form "WIN X", make sure to use exactly one space character.

### Constraints

-moves contains an odd number of elements
-moves contains between one and seven elements, inclusive
-each element in moves is between 1 and 9, inclusive
-moves contains no duplicates
-moves describes a game of Fifteen that is in progress, meaning that neither player has made 15 yet

### Examples

0)

 `{7, 5, 9, 6, 8, 1, 2}`
`Returns: "WIN 4"`
 The dealer has covered 7, 9, 8, and 2, while the patron has covered 5, 6, and 1. The sole remaining numerals are 4 and 3. If the patron covers the 3, he fails to make 15. But covering 4 wins him the game, since 5+6+4=15.
1)

 `{4, 8, 6, 5, 2}`
`Returns: "LOSE"`
 The available numerals are 1, 3, 7, and 9. If the patron's choice is something other than 9, the dealer can win on his next turn because 4+2+9=15. But if the patron covers the 9, the dealer can next play 7, which wins the game because 6+2+7=15. Either way, the patron is doomed.
2)

 `{2, 4, 7, 6, 9, 8, 5}`
`Returns: "WIN 1"`
 The patron wins either by covering 1, which yields 6+8+1=15, or by covering 3 to make 4+8+3=15. Since lower numerical values are preferred, we settle on 1.
3)

 `{9, 2, 1, 6, 3, 4, 8}`
`Returns: "WIN 5"`
 The patron can win by covering 5 or 7, so we choose 5.
4)

 `{1}`
`Returns: "LOSE"`
5)

 `{6, 3, 7, 8, 1}`
`Returns: "WIN 2"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1850

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4665&pm=1850

Eeyore

#### Testers:

lbackstrom , brett1479

#### Problem categories:

Recursion, Search