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. In the first sample the game went like this: