# The “Win-stay and Lose-shift” Strategy

In recent weeks, geek tabloids have hit the newsstands around the world with a truly remarkable breakthrough in science: a group of researchers from Chinese universities have written a paper about the role of psychology in winning (or losing) at rock-paper-scissors (RPS). After studying how players change or keep their strategies during multiple-round sessions, the scientists figured out a basic rule that people tend to play by that could potentially be exploited. This rule is called the win-stay and lose-shift strategy. An RPS session is a finite sequence of rounds played between two opponents. In each round, players simultaneously form one of three shapes with an outstretched hand: rock (R), paper (P), and scissors (S). Rock beats scissors, scissors beat paper, and paper beats rock; if both players throw the same shape, the round is tied. The outcome of a round for a player is 1 point if he/she wins, −1 point if he/she loses, and 0 points if it is a tie. The outcome of a session for a player is the sum over the outcome points of his/her rounds. For example, assume that a and b are playing a session of three rounds. In the first round a plays scissors and b plays paper; in the second round a plays paper and b plays paper; and, in the last round a plays rock and b plays rock. Then, the outcome of the first round for a is 1 point (for b is −1 point), and the outcomes of the second and third rounds for a is 0 points (for b is also 0 points). Consequently, the outcome of this session for a is 1 point and for b is −1 point. During an RPS session, the win-stay and lose-shift strategy for a player p is as follows: • If it is the first round or if it was a tie in the previous round, for the current round p makes a guess. • If p lost in the previous round, for the current round p switches to the thing that beats p’s opponent previous choice. • If p won in the previous round, for the current round p switches to the thing that beats p’s previous choice. For example, assume that a and b are playing a session of three rounds, and a is playing under the win-stay and lose-shift strategy and that b plays as above. Initially a guesses R and loses (P beats R). In the second round a switches to S because it beats b’s previous winning choice (i.e., P) and wins (S beats P). In the third round a switches to R because it beats a’s previous choice (i.e., S) and ties (b also plays R). In this session the outcome for a is 0 points. However, this is not the only possible outcome for a under the win-stay and lose-shift strategy. Given a session of n rounds for players a and b, and the probabilities of a guessing R, P, and S during the session, you are asked to write a program that decides if a’s expected session outcome when playing under the win-stay and lose-shift strategy against b is better than a’s actual session outcome. Input The first line of the input contains a non-negative integer number N (N ≥ 0) indicating the number of test cases. Then N test cases follow, each consisting of three lines of input. The first and second lines of a test case contain, respectively, strings a and b only containing characters R, P, and S (1 ≤ |a| ≤ 104, 1 ≤ |b| ≤ 104, with |a| = |b|) defining an RPS session of |a| rounds played between players a and b. The third line of a test case contains three blank-separated integer numbers pR, pP , and pS (0 ≤ pR ≤ 100, 0 ≤ pP ≤ 100, 0 ≤ pS ≤ 100, with pR + pP + pS = 100) indicating, respectively, the probability (amplified by 100) of a guessing rock, scissors, and paper.

2/2 Output For each test case output a single line containing three blank-separated quantities of the form xyz where • x is an integer indicating a’s actual session outcome against b, • y is a floating point number indicating a’s expected session outcome when playing against b with probabilities pR, pP , and pS under the win-stay and lose-shift strategy (rounded up to exactly 4 decimal places, with no leading zeroes but at least one digit before the decimal point), and • z is the character ‘Y’ if y is strictly greater than x, and ‘N’, otherwise. Sample Input 4 SPR PPR 5 80 15 RRR PPR 5 80 15 S S 33 34 33 S S 34 33 33 Sample Output 1 0.3060 N -2 0.3060 Y 0 -0.0100 N 0 0.0100 Y