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 math
def lcm(x, y):
    if x > y:
        z = x
    else:
        z = y
    while(True):
        if((z % x == 0) and (z % y == 0)):
            lcm = z
            break
        z += 1
    return lcm
Nikif = 0
Policarf = 0
games = int(input())
Nikiffs_sequence = str(input())
Policarf_sequence = str(input())
def solution(Nikif,Policarf,games,Nikiffs_sequence,Policarf_sequence):
    Policarf_sequence = list(Policarf_sequence)
    Nikiffs_sequence =  list(Nikiffs_sequence)
#     Policarf_sequence.remove("\n")
#     Nikiffs_sequence.remove("\n")
    LCM = lcm(len(Nikiffs_sequence),len(Policarf_sequence))
    #print(LCM)
    
#     while len(Nikiffs_sequence) < LCM:
#         Nikiffs_sequence+=Nikiffs_sequence
#     while len(Policarf_sequence) < LCM:
#         Policarf_sequence+=Policarf_sequence
    Nikiffs_sequence = Nikiffs_sequence*(LCM//len(Nikiffs_sequence))
    Policarf_sequence = Policarf_sequence*(LCM//len(Policarf_sequence))
    new_list = list(zip(Nikiffs_sequence,Policarf_sequence))
    Nikif_count = 0
    Policarf_count = 0 
    for i in range(len(new_list)):
        if new_list[i][0] == new_list[i][1]:
            pass
        elif new_list[i][0] == "R" and new_list[i][1] == "S":
            Nikif_count+=1
        elif new_list[i][0] == "S" and new_list[i][1] == "P":
            Nikif_count+=1
        elif new_list[i][0] == "P" and new_list[i][1] == "R":
            Nikif_count+=1
        else:
            Policarf_count+=1
    if games<LCM or games == LCM:
        for i in range(games):
            if new_list[i][0] == new_list[i][1]:
                pass
            elif new_list[i][0] == "R" and new_list[i][1] == "S":
                Nikif+=1
            elif new_list[i][0] == "S" and new_list[i][1] == "P":
                Nikif+=1
            elif new_list[i][0] == "P" and new_list[i][1] == "R":
                Nikif+=1
            else:
                Policarf+=1
    elif games>LCM:
        if games % LCM == 0:
            Policarf = Policarf_count*(games//LCM)
            Nikif = Nikif_count*(games//LCM)
            return print(Policarf,Nikif)

        else:
            Policarf = Policarf_count*(games//LCM)
            Nikif = Nikif_count*(games//LCM)
            for i in range(games%LCM):
                if new_list[i][0] == new_list[i][1]:
                    pass
                elif new_list[i][0] == "R" and new_list[i][1] == "S":
                    Nikif+=1
                elif new_list[i][0] == "S" and new_list[i][1] == "P":
                    Nikif+=1
                elif new_list[i][0] == "P" and new_list[i][1] == "R":
                    Nikif+=1
                else:
                    Policarf+=1 
            return print(Policarf,Nikif)
        
  
    return print(Policarf,Nikif)#,"_________________________________________",len(Nikiffs_sequence),len(Policarf_sequence), Nikiffs_sequence,Policarf_sequence)
    
solution(Nikif,Policarf,games,Nikiffs_sequence,Policarf_sequence)
        