[USACO10MAR] StarCowraft G

The beta version of StarCowraft II is ready! Farmer John and Bessie are testing it, trying different strategies in one-on-one battles against each other's armies. The goal in StarCowraft II is to defeat your opponent's army in a battle. Each player's army fights in a battle. An army comprises as many as three different types of 'units' with respective strengths denoted by constant positive real numbers unknown to the players: cattlebruisers with strength S1, cow templars with strength S2, and ultracows with strength S3. The only given bounding information is that no unit is more than 100 times as strong as any another unit. An army's total strength is the sum of the individual strengths of each of its units. An army that has, among others units, 23 cattlebruisers would gain 23\*S1 strength just from the cattlebruisers. When two opposing armies fight in a battle, the army with a higher total strength value wins. If the armies have exactly equal strength values, one of the players randomly wins. Farmer John and Bessie played N (0 <= N <= 300) 'test battles'. In the i-th test battle, FJ's army had J1\_i cattlebruisers, J2\_i cow templars, and J3\_i ultracows (0 <= J1\_i + J2\_i + J3\_i <= 1,000). Similarly, Bessie's army had B1\_i cattlebruisers, B2\_i cow templars, and B3\_i ultracows (0 <= B1\_i + B2\_i + B3\_i <= 1,000). After their armies fought against each other, FJ and Bessie recorded the winner as a single 'victory letter' V\_i: 'J' if Farm John won the battle; 'B' if Bessie won. Although these victory results are the only information that they have, they hope to predict some of the results of additional battles if they are given the unit compositions of two opposing armies. For some battles, though, they know it might not be possible to determine the winner with certainty. Given the results of the N test battles that Farmer John and Bessie already played, write a program that decides the winner (if possible) for M (1 <= M <= 2,000) new battles. The results reported for the test battles are correct; there exists at least one set of strength values which are consistent with the results. For purposes of demonstrating the army strength evaluation functions, consider these test battles fought in a game where we (but neither FJ nor Bessie) know that S1=9.0, S2=7.0, and S3=4.0: ```cpp ---- Farmer John ---- ------- Bessie ------ Battle J1 J2 J3 J_Strength B1 B2 B3 B_Strength Outcome 6 5 4 105 5 4 7 101 J 5 4 2 81 3 5 5 82 B 9 0 10 121 8 2 7 114 J ``` These results connote the following deduced results for the reasons shown: ---- Farmer John ---- ------- Bessie ------ Battle J1 J2 J3 J\_Strength B1 B2 B3 B\_Strength Outcome 6 6 4 112 5 4 7 101 J FJ's army is even stronger than in test battle 1 9 0 10 121 8 2 6 110 J Bessie's army is even weaker than in test battle 3 《星际争霸2》全面公测啦！Farmer John和Bessie正在测试中——在1v1的战役中使用一些不同的策略来对抗对方的部队。《星际争霸2》的游戏目标就是在战役中打败你对手的军队。 每个选手的军队都在战役中拼杀。一支军队由若干3种不同类型的单位所组成，不同单位有着不同的由正实数表示的，且不被选手所知道的力量值：cattlebruisers 的力量是S1，cow templars 的力量是S2，ultracows的力量是S3。唯一提供的信息是，没有一个单位的力量值超过另一个单位力量值的100倍。 一支军队的总力量值，是其中各自单独的单位的力量值的总和。比如一支军队除了其他单位有23个cattlebruisers，那么这支军队单独从cattlebruisers就能获得23\*S1的力量值。 当两支对立的军队在战役中厮杀，有着更高力量值的军队将获得胜利。如果两支军队的力量值恰好相同，那么将随机产生一个获胜方。 Farmer John 和 Bessie 进行了 N (0 <= N <= 300) 局的“测试战役”。在第 i 局测试战役中，Farmer John 有 J1\_i 个 cattlebruisers，J2\_i 个 cow templars 以及 J3\_i 个 ultracows(0 <= J1\_i + J2\_i + J3\_i <= 1,000)。相似的，Bessie的军队有 B1\_i 个 cattlebruisers，B2\_i 个 cow templars 以及 B3\_i 个 ultracows (0 <= B1\_i + B2\_i + B3\_i <= 1,000)。当他们的军队战斗结束后，FJ 和 Bessie 将胜者以一个单独的“胜利字母” V\_i 记录下来："J"表示 Farmer John 赢得了战役；"B" 表示 Bessie 获胜了。 虽然这些结果是他们唯一所拥有的信息，但是他们希望预测一些额外的战役的结果——如果告知他们两支对立军队的组成。尽管，可能对于一些比赛他们是无法确定到底哪一方一定能获胜的。 给出已经结束的 N 场测试战役的结果，写一个程序来确定(如果可能的话)M (1 <=M <=2,000)场额外战役的获胜方。 所有给出的测试战役的结果都是正确的。至少存在一种合法的力量值的取值符合这些结果。

\* Line 1: Two space-separated integers: N and M \* Lines 2..N+1: Line i+1 describes a test battle with seven space-separated items -- a victory letter and six space-separated integer unit counts: V\_i, J1\_i, J2\_i, J3\_i, B1\_i, B2\_i, and B3\_i \* Lines N+2..N+M+1: Line i+N+1 describes a 'new battle' using six space-separated integers: J1\_i, J2\_i, J3\_i, B1\_i, B2\_i, and B3\_i

\* Lines 1..M: Line i contains the outcome of the i-th new battle: 'J' if Farmer John definitely wins, 'B' if Bessie definitely wins, and 'U' (undecidable) if it is impossible to decide the winner with the given information.

3 3 
J 6 5 4 5 4 7 
B 5 4 2 3 5 5 
J 9 0 10 8 2 7 
6 6 4 5 4 7 
9 0 10 8 2 6 
3 4 8 4 4 6 

J 
J 
U 

First two games correspond to the examples in the description. The result of the last game cannot be determined with only the information that Farmer John and Bessie currently have. Specifically, both S\_1=9.0, S\_2=7.0, S\_3=4.0 and S\_1=12.0, S\_2=20.0, S\_3=10.0 are consistent with the &quot;test battles,&quot; but they give different results when plugged in the third &quot;new battle.&quot;