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):
    while a != b:
        if a > b:
            a -= b
        else:
            b -= a
    
    return a

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

def solve():
    rounds = int(raw_input())
    str_a  = raw_input()
    str_b  = raw_input()
    
    len_a = len(str_a)
    len_b = len(str_b)
    
    pos_a = 0
    pos_b = 0
    
    spots_a = 0
    spots_b = 0
    
    cyc_spots_a = 0
    cyc_spots_b = 0
    
    lcm_val = lcm(len_a, len_b)
    num_cycles = rounds / lcm_val
    rem_rounds = rounds - (num_cycles * lcm_val)
    for i in range(lcm_val):
        c = str_a[pos_a] + str_b[pos_b]
        if c == 'RS' or c == 'PR' or c == 'SP':
            cyc_spots_b += 1
        elif c == 'RP' or c == 'PS' or c == 'SR':
            cyc_spots_a += 1
            
        if i == (rem_rounds - 1):
            spots_a = cyc_spots_a
            spots_b = cyc_spots_b
        
        pos_a = (pos_a + 1) % len_a
        pos_b = (pos_b + 1) % len_b
    
    spots_a += (cyc_spots_a * num_cycles)
    spots_b += (cyc_spots_b * num_cycles)
        
    print "%d %d" % (spots_a, spots_b) 
                        
if __name__ == '__main__':
    solve()