Rock-Paper-Scissors

- 有两个人在玩石头剪刀布游戏： R-石头 P-布 S-剪刀 每个人都会按照一个周期出石头，剪刀或布。 周期肯定在1000以内（包括1000）问玩n把后， 双方各**输**了多少次。 - 输入第一行一个n,（1<=n<=2*10^9）n为玩了几把 第2行为第一个人的周期规律 第3行为第二个人的周期规律 - 输出共2个数：第一个人输的次数和第二个人输的次数

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.

7
RPS
RSPP

3 2

5
RRRRRRRR
R

0 0

In the first sample the game went like this: - R - R. Draw. - P - S. Nikephoros loses. - S - P. Polycarpus loses. - R - P. Nikephoros loses. - P - R. Polycarpus loses. - S - S. Draw. - R - P. Nikephoros loses. Thus, in total Nikephoros has $ 3 $ losses (and $ 3 $ red spots), and Polycarpus only has $ 2 $ .