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.
def gcd(a, b):
    return a if b == 0 else gcd(b, a % b)

def arb(f, s):
    if (f, s) == ('R', 'S') or (f, s) == ('S', 'P') or (f, s) == ('P', 'R'):
        return 2
    elif (f, s) == ('R', 'R') or (f, s) == ('S', 'S') or (f, s) == ('P', 'P'):
        return 0
    else:
        return 1

n, nikif, polik = int(raw_input()), raw_input(), raw_input()
nikif_len, polik_len = len(nikif), len(polik)
nod = gcd(nikif_len, polik_len)
nok = nikif_len * polik_len / nod
i=0
out = [0, 0]
chastnoe, ostatok = divmod(n, nok)
while i < ostatok:
    cur_res = arb(nikif[i % nikif_len], polik[i % polik_len])
    if cur_res != 0:
        out[cur_res - 1] += 1
    i += 1
if chastnoe == 0:
    print out[0], out[1]
else:
    out[0], out[1] = out[0] * (chastnoe + 1), out[1] * (chastnoe + 1)
    while i < nok:
        cur_res = arb(nikif[i % nikif_len], polik[i % polik_len])
        if cur_res != 0:
            out[cur_res - 1] += chastnoe
        i += 1
    print out[0], out[1]
