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.
n = input()
A = raw_input().strip()
A0 = A
# print A
B = raw_input().strip()
B0 = B

lena = len(A)
lenb = len(B)
mk = lena * lenb
while len(A) < mk:
	A += A0
while len(B) < mk:
	B += B0

c = 0
d = 0
C = []
for i in range(mk):
	ai = A[i]
	bi = B[i]
	# print ai,'VS',bi,
	if ai == 'R':
		if bi == 'P':
			c += 1
			C += ['1']
			# print '->','Polycarpus',
		elif bi == 'S':
			d += 1
			C += ['2']
			# print '->','Nikephoros',
		else:
			C += ['0']
	elif ai == 'P':
		if bi == 'R':
			d += 1
			C += ['2']
			# print '->','Nikephoros',
		elif bi == 'S':
			c += 1
			C += ['1']
			# print '->','Polycarpus',
		else:
			C += ['0']
	elif ai == 'S':
		if bi == 'R':
			c += 1
			C += ['1']
			# print '->','Polycarpus',
		elif bi == 'P':
			d += 1
			C += ['2']
			# print '->','Nikephoros',
		else:
			C += ['0']
	else:
		C += ['0']
	# print
ans1 = c*(n/mk)
ans2 = d*(n/mk)
for i in range(n%mk):
	ci = C[i]
	if ci == '1':
		ans1 += 1
	elif ci == '2':
		ans2 += 1
print ans1,ans2