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 urllib
import random

#if( len(sys.argv) != 3 ):
#    print "Usage app.py (input file) (output file)"

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def mcd(n, m):
    return (n/gcd(n,m))*m

n = int(sys.stdin.readline())
a = sys.stdin.readline()[:-1]
b = sys.stdin.readline()[:-1]
sa = 0
sb = 0
nok = mcd(len(a), len(b))
repeat_count = n / nok
nbalance = n % nok
balance_a = 0
balance_b = 0
for i in range(nok):
    ia = i % len(a)
    ib = i % len(b)
    if(a[ia] == 'R'):
        if(b[ib] == 'S'):
            sb = sb + 1
        elif(b[ib] == 'P'):
            sa = sa + 1
    elif(a[ia] == 'S'):
        if(b[ib] == 'R'):
            sa = sa + 1
        elif(b[ib] == 'P'):
            sb = sb + 1
    else:#a[i] == 'P'
        if(b[ib] == 'R'):
            sb = sb + 1
        elif(b[ib] == 'S'):
            sa = sa + 1
    if(i == nbalance-1):
        balance_a = sa
        balance_b = sb

sa = repeat_count * sa + balance_a
sb = repeat_count * sb + balance_b

print "%i %i" % (sa, sb)
