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 Rock {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int i,j,n,l,l1,k,sum,sum1,l3,n1,n2;
        String s,s1,s2;
        while (input.hasNext()){
            n = input.nextInt(); s = input.nextLine(); sum = 0;sum1 = 0;
            s1 = input.nextLine(); s2 = input.nextLine();
            l = s1.length(); l1 = s2.length();
            l3 = Math.max(l,l1);
            if (l3 >= n) {
                for (i = 0, j = 0, k = 0; i < n; i++) {
                    if ((s1.charAt(j) == 'R' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'S' && s2.charAt(k) == 'P') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'R')) {
                        sum++;
                    }
                    if ((s1.charAt(j) == 'S' && s2.charAt(k) == 'R') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'R' && s2.charAt(k) == 'P')) {
                        sum1++;
                    }

                    if (j == l - 1) j = -1;
                    if (k == l1 - 1) k = -1;
                    j++;
                    k++;
                }
                System.out.println(sum1 + " " + sum);
            }
            else {

             /*   if (l /l1 == 2 || l1/l == 2){
                    if (l > l1){
                        l3 = l - l1;
                        for (i=0; i<l3; i++){
                            s2 += s2.charAt(i);
                        }
                    }
                    else {
                        l3 = l1 -l;
                        for (i=0; i<l3; i++)
                            s1 += s1.charAt(i);
                    }
                    l = s1.length();
                    l1 = s2.length();
                    System.out.println("sdfgyu");

                }*/

                if (l != l1){
                    l3 = l * l1;
                    for (i = 0, j = 0, k = 0; i < l3; i++) {
                        if ((s1.charAt(j) == 'R' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'S' && s2.charAt(k) == 'P') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'R')) {
                            sum++;
                        }
                        if ((s1.charAt(j) == 'S' && s2.charAt(k) == 'R') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'R' && s2.charAt(k) == 'P')) {
                            sum1++;
                        }

                        if (j == l - 1) j = -1;
                        if (k == l1 - 1) k = -1;
                        j++;
                        k++;
                    }

                    sum = (sum * (n / l3));
                    sum1 = (sum1 * (n / l3));
                   // System.out.println(sum1 + " " + sum);//jhgfd

                    n1 = n % l3;
                    for (i = 0, j = 0, k = 0; i < n1; i++) {
                        if ((s1.charAt(j) == 'R' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'S' && s2.charAt(k) == 'P') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'R')) {
                            sum++;
                        }
                        if ((s1.charAt(j) == 'S' && s2.charAt(k) == 'R') || (s1.charAt(j) == 'P' && s2.charAt(k) == 'S') || (s1.charAt(j) == 'R' && s2.charAt(k) == 'P')) {
                            sum1++;
                        }

                        if (j == l - 1) j = -1;
                        if (k == l1 - 1) k = -1;
                        j++;
                        k++;
                    }
                }

                if (l1 == l){
                    for (i = 0; i < l; i++) {
                        if ((s1.charAt(i) == 'R' && s2.charAt(i) == 'S') || (s1.charAt(i) == 'S' && s2.charAt(i) == 'P') || (s1.charAt(i) == 'P' && s2.charAt(i) == 'R')) {
                            sum++;
                        }
                        if ((s1.charAt(i) == 'S' && s2.charAt(i) == 'R') || (s1.charAt(i) == 'P' && s2.charAt(i) == 'S') || (s1.charAt(i) == 'R' && s2.charAt(i) == 'P')) {
                            sum1++;
                        }
                    }
                    n1 = n / l1;
                    n2 = n % l1;
                    sum *= n1; sum1 *= n1;
                    for (i=0; i<n2; i++){
                        if ((s1.charAt(i) == 'R' && s2.charAt(i) == 'S') || (s1.charAt(i) == 'S' && s2.charAt(i) == 'P') || (s1.charAt(i) == 'P' && s2.charAt(i) == 'R')) {
                            sum++;
                        }
                        if ((s1.charAt(i) == 'S' && s2.charAt(i) == 'R') || (s1.charAt(i) == 'P' && s2.charAt(i) == 'S') || (s1.charAt(i) == 'R' && s2.charAt(i) == 'P')) {
                            sum1++;
                        }
                    }
                }
                System.out.println(sum1 + " " + sum);
            }
        }
    }
}
