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

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.

Examples

Input

7
RPS
RSPP


Output

3 2

Input

5
RRRRRRRR
R


Output

0 0

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.
import java.util.Scanner;


public class Main {
    public static void main(String[] args) {
        Scanner r = new Scanner(System.in);
        
        int N = r.nextInt();
        
        char[] a = r.next().toCharArray();
        char[] b = r.next().toCharArray();
        
        
        char[][] S = new char[300][300];
        
        S['P']['S'] = 2;
        S['S']['P'] = 1;
        S['R']['P'] = 2;
        S['P']['R'] = 1;
        S['S']['R'] = 2;
        S['R']['S'] = 1;
        S['R']['R'] = 0;
        S['S']['S'] = 0;
        S['P']['P'] = 0;
        
        int[][] R = new int[lcm(a.length, b.length)][3];
        for(int i = 0; i < lcm(a.length, b.length); i++){
            R[i][S[a[i % a.length]][b[i % b.length]]]++;
        }
        
        int m = N / lcm(a.length, b.length);
        int[] X = new int[3];
        for(int i = 0; i < lcm(a.length, b.length); i++)
            X[S[a[i % a.length]][b[i % b.length]]] += m;
        
        for(int i = 0; i < N % lcm(a.length, b.length); i++)
            X[S[a[i % a.length]][b[i % b.length]]]++;
        
        System.out.println(X[2] + " " + X[1]);
    }

    private static int lcm(int x, int y) {
        int ret = x * (y / gcd(x, y));
        return ret;
    }

    private static int gcd(int x, int y) {
        if(y == 0)return x;
        else return gcd(y, x % y);
    }
}
