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 sys
import math

n = int(sys.stdin.readline())
am = sys.stdin.readline()
lam = len(am) - 1
bk = sys.stdin.readline()
lbk = len(bk) - 1

resam = 0
resbk = 0
x = 0
z = 0

ssr = [(0, 0)]
vv = n
if(lam * lbk < n):
    vv = lam * lbk

for i in range(vv):
    
    if(x >= lam):
        x = 0
    
    if(z >= lbk):
        z = 0
        
    if(am[x] == bk[z]):
        x += 1
        z += 1
        ssr.append((resam, resbk))
        continue  
      
    if((am[x] == 'S' or am[x] == 'P') and (bk[z] == 'S' or bk[z] == 'P')):
        if(am[x] < bk[z]):
            resam += 1
        else:
            resbk += 1
    else:
        if(am[x] > bk[z]):
            resam += 1
        else:
            resbk += 1
            
    x += 1
    z += 1
    
    ssr.append((resam, resbk))

   
if(lam * lbk < n):
    y = int(n / (lam * lbk))
    resam *= y
    resbk *= y
    ty = ssr[n % (lam * lbk)]
    resam += ty[0]
    resbk += ty[1]
        
            
print(resam, resbk)

    
    