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 get_lcm(n1, n2):
    # find gcd
    gcd = math.gcd(n1, n2)

    # formula
    result = (n1 * n2) / gcd
    return result


class CodeforcesTask173ASolution:
    def __init__(self):
        self.result = ''
        self.rounds = 0
        self.n_str = ''
        self.p_str = ''

    def read_input(self):
        self.rounds = int(input())
        self.n_str = input()
        self.p_str = input()

    def process_task(self):
        n = int(len(self.n_str))
        k = int(len(self.p_str))
        ap = 0
        bp = 0
        np = 0
        pp = 0
        full_round = int(get_lcm(n, k))
        if self.rounds <= full_round:
            for x in range(self.rounds):
                a = self.n_str[ap]
                b = self.p_str[bp]
                ap += 1
                bp += 1
                if ap >= n:
                    ap = 0
                if bp >= k:
                    bp = 0
                if (a == "R" and b == "S") or (a == "S" and b == "P") or (a == "P" and b == "R"):
                    pp += 1
                elif (b == "R" and a == "S") or (b == "S" and a == "P") or (b == "P" and a == "R"):
                    np += 1
            self.result = "{0} {1}".format(np, pp)
        else:
            for x in range(full_round):
                a = self.n_str[ap]
                b = self.p_str[bp]
                ap += 1
                bp += 1
                if ap >= n:
                    ap = 0
                if bp >= k:
                    bp = 0
                if (a == "R" and b == "S") or (a == "S" and b == "P") or (a == "P" and b == "R"):
                    pp += 1
                elif (b == "R" and a == "S") or (b == "S" and a == "P") or (b == "P" and a == "R"):
                    np += 1
            np *= self.rounds // full_round
            pp *= self.rounds // full_round
            for x in range(self.rounds % full_round):
                a = self.n_str[ap]
                b = self.p_str[bp]
                ap += 1
                bp += 1
                if ap >= n:
                    ap = 0
                if bp >= k:
                    bp = 0
                if (a == "R" and b == "S") or (a == "S" and b == "P") or (a == "P" and b == "R"):
                    pp += 1
                elif (b == "R" and a == "S") or (b == "S" and a == "P") or (b == "P" and a == "R"):
                    np += 1
            self.result = "{0} {1}".format(np, pp)

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask173ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
