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());

aa = raw_input();
bb = raw_input();

laa = len(aa)
lbb = len(bb)

def gcd(x, y):
    if (y == 0):
        return x
    else:
        return gcd(y, x % y)

def lcm(x, y):
    return x / gcd(x, y) * y

m = lcm(laa, lbb)
  
def work(mm):
    i = 0
    a = 0
    b = 0
    while i < mm:
        j = i % laa
        k = i % lbb
        if (aa[j] == bb[k]):
            pass
        elif (aa[j] == 'R'):
            if (bb[k] == 'P'):
                a += 1 
            else:
                b += 1
        elif (aa[j] == 'P'):
            if (bb[k] == 'R'):
                b += 1
            else:
                a += 1
        else: # S
            if (bb[k] == 'R'):
                a += 1
            else:
                b += 1
        i += 1
    return [a, b]

la = 0
lb = 0

mm = work(m)
a = mm[0]
b = mm[1]

aaa = 0
bbb = 0
k = n % m
if (k == 0):
    la = a * n / m
    lb = b * n / m
elif (n > m):
    mm = work(k)
    aaa = mm[0]
    bbb = mm[1]
    la = a * (n / m) + aaa
    lb = b * (n / m) + bbb  
else:
    mm = work(n)
    aaa = mm[0]
    bbb = mm[1]
    la = aaa
    lb = bbb
    
print la, " ", lb
    
