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 = (a₁, a₂, ..., 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: a₁, a₂, ..., a_m, a₁, a₂, ..., a_m, a₁, ... and so on. Polycarpus had a similar strategy, only he had his own sequence of items B = (b₁, b₂, ..., 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.

Input

The first line contains integer n (1 ≤ n ≤ 2·10⁹) — 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.

Output

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

Note

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.

Rock-Paper-Scissors

Examples