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 sys

rounds=int(sys.stdin.readline().strip('\n'))

def Solution():
    global rounds
    s_A=list(map(str, sys.stdin.readline().rstrip('\n')))
    s_B=list(map(str, sys.stdin.readline().rstrip('\n')))

    if rounds<=len(s_A):
        s_A=s_A[0:rounds]
        if rounds<len(s_B):
            s_B=s_B[0:rounds]
            return Prepare(s_A, s_B) 
        return Prepare(s_A, s_B)
    elif rounds<len(s_B):
        s_B=s_B[0:rounds]
        if rounds<len(s_B):
            s_A=s_A[0:rounds]
            return Prepare(s_A, s_B)
        return Prepare(s_A, s_B)
    else:
        return Prepare(s_A, s_B)


def Prepare(s_A, s_B):
    if len(s_A)==len(s_B):
        return Compare(s_A, s_B)

    else:
        if len(s_A)>len(s_B):
            greater = len(s_A)
        else:
            greater = len(s_B)

        while(True):
            if((greater % len(s_A) == 0) and (greater % len(s_B) == 0)):
                lcm = greater
                break
            greater += 1
        Alcm=lcm//len(s_A)
        Blcm=lcm//len(s_B)
        return Compare(s_A*Alcm, s_B*Blcm)



def Compare(s_A, s_B):
    global rounds

    zipped=list(zip(s_A, s_B))
    Nikephoros=0
    Polycarpus=0
    mult=1
    for i in range (0, len(zipped)):
        if rounds==i:
            return print (Polycarpus*mult, Nikephoros*mult)
        elif zipped[i][0]==zipped[i][1]:
            pass
        elif (zipped[i][0]=="S" and zipped[i][1]=="P") or \
        (zipped[i][0]=="R" and zipped[i][1]=="S") or \
        (zipped[i][0]=="P" and zipped[i][1]=="R"):
            Nikephoros+=1
        else:
            Polycarpus+=1
    
    if rounds%len(zipped)==0:
        mult=rounds//len(zipped)
        print (Polycarpus*mult, Nikephoros*mult)

    else:
        mult=rounds//len(zipped)
        Nikephoros_add=0
        Polycarpus_add=0
        fraction=rounds - (len(zipped)*mult)
        iter=0
        for i in range (0, len(zipped)):
            if iter==fraction:
                return print(Polycarpus*mult + Polycarpus_add, Nikephoros*mult+ Nikephoros_add)
            elif zipped[i][0]==zipped[i][1]:
                iter+=1
                pass
            elif (zipped[i][0]=="S" and zipped[i][1]=="P") or \
            (zipped[i][0]=="R" and zipped[i][1]=="S") or \
            (zipped[i][0]=="P" and zipped[i][1]=="R"):
                Nikephoros_add+=1
                iter+=1
            else:
                Polycarpus_add+=1
                iter+=1

        


Solution()