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 A {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        sc.nextLine();
        String str1 = sc.nextLine();
        String str2 = sc.nextLine();
        char[] mas1 = str1.toCharArray();
        char[] mas2 = str2.toCharArray();
        int sh1=0,sh2=0;
        int index1=0,index2=0;
        int i;
        for(i=0; i<n; i++){
            if (index1==0&&index2==0&&i!=0) break;
            if (mas1[index1]==mas2[index2]) {
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            if (mas1[index1]=='R' && mas2[index2]=='S'){
                sh2++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                
                continue;
            }
            if (mas1[index1]=='R' && mas2[index2]=='P'){
                sh1++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            if (mas1[index1]=='P' && mas2[index2]=='S'){
                sh1++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            if (mas1[index1]=='P' && mas2[index2]=='R'){
                sh2++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            if (mas1[index1]=='S' && mas2[index2]=='R'){
                sh1++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            if (mas1[index1]=='S' && mas2[index2]=='P'){
                sh2++;
                index1++;
                index2++;
                if (index1>str1.length()-1) index1=0;
                if (index2>str2.length()-1) index2=0;
                continue;
            }
            
        }
        if (i==n-1)
        System.out.println(sh1+" "+sh2);
        else {
            int t = n%i;
            int k = n/i;
            int ch1=0,ch2=0;
            for(i=0; i<t; i++){
                if (mas1[index1]==mas2[index2]) {
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                if (mas1[index1]=='R' && mas2[index2]=='S'){
                    ch2++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    
                    continue;
                }
                if (mas1[index1]=='R' && mas2[index2]=='P'){
                    ch1++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                if (mas1[index1]=='P' && mas2[index2]=='S'){
                    ch1++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                if (mas1[index1]=='P' && mas2[index2]=='R'){
                    ch2++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                if (mas1[index1]=='S' && mas2[index2]=='R'){
                    ch1++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                if (mas1[index1]=='S' && mas2[index2]=='P'){
                    ch2++;
                    index1++;
                    index2++;
                    if (index1>str1.length()-1) index1=0;
                    if (index2>str2.length()-1) index2=0;
                    continue;
                }
                
            }
            System.out.println((k*sh1+ch1)+" "+(k*sh2+ch2));
            }
        }

}
