A8550 | Rock-Paper-Scissors

Nikephoros and Polycarpus play rock-paper-scissors. The loser gets pinched (not too severely!).

Let us remind you the rules of this game. Rock-paper-scissors is played by two players. In each round the players choose one of three items independently from each other. They show the items with their hands: a rock, scissors or paper. The winner is determined by the following rules: the rock beats the scissors, the scissors beat the paper and the paper beats the rock. If the players choose the same item, the round finishes with a draw.

Nikephoros and Polycarpus have played $n$ rounds. In each round the winner gave the loser a friendly pinch and the loser ended up with a fresh and new red spot on his body. If the round finished in a draw, the players did nothing and just played on.

Nikephoros turned out to have worked out the following strategy: before the game began, he chose some sequence of items $A=(a_{1},a_{2},...,a_{m})$ , and then he cyclically showed the items from this sequence, starting from the first one. Cyclically means that Nikephoros shows signs in the following order: $a_{1}$ , $a_{2}$ , $...$ , $a_{m}$ , $a_{1}$ , $a_{2}$ , $...$ , $a_{m}$ , $a_{1}$ , $...$ and so on. Polycarpus had a similar strategy, only he had his own sequence of items $B=(b_{1},b_{2},...,b_{k})$ .

Determine the number of red spots on both players after they've played $n$ rounds of the game. You can consider that when the game began, the boys had no red spots on them.

The first line contains integer $n$ ( $1<=n<=2·10^{9}$ ) — the number of the game's rounds.

The second line contains sequence $A$ as a string of $m$ characters and the third line contains sequence $B$ as a string of $k$ characters ( $1<=m,k<=1000$ ). The given lines only contain characters "R", "S" and "P". Character "R" stands for the rock, character "S" represents the scissors and "P" represents the paper.

Print two space-separated integers: the numbers of red spots Nikephoros and Polycarpus have.