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.
n=int(raw_input())
Nike=raw_input()
Poly=raw_input()
a,b=max(len(Nike),len(Poly)),min(len(Nike),len(Poly))


def gcd(a,b):
    while a%b:
        a,b=b,a%b
    return b

def lcm(a,b):
    return a*b/gcd(a,b)

chk=lcm(a,b)


def play(m,Nike,Poly):
    ni=po=0
    for i in range(m):
        if Nike[i%len(Nike)]=='R' and Poly[i%len(Poly)]=='S':
            po+=1
        elif Nike[i%len(Nike)]=='R' and Poly[i%len(Poly)]=='P':
            ni+=1
        elif Nike[i%len(Nike)]=='S' and Poly[i%len(Poly)]=='R':
            ni+=1
        elif Nike[i%len(Nike)]=='S' and Poly[i%len(Poly)]=='P':
            po+=1
        elif Nike[i%len(Nike)]=='P' and Poly[i%len(Poly)]=='S':
            ni+=1
        elif Nike[i%len(Nike)]=='P' and Poly[i%len(Poly)]=='R':
            po+=1
    return ni,po



if n<=chk:
    ans=play(n,Nike,Poly)
    print ans[0],ans[1]
else:
    t=n/chk
    k=n%chk
    ta=play(chk,Nike,Poly)
    ka=play(k,Nike,Poly)
    print (ta[0]*t)+ka[0],(ta[1]*t)+ka[1]