173_A. Rock-Paper-Scissors
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.
```python
n = int(input())
a = input()
b = input()
ai = 0
alen = len(a)
bi = 0
blen = len(b)
nik = 0
pol = 0
if alen == blen: rnd = alen
else: rnd = alen*blen
numofrounds = 0
for i in range(n):
    #print(i,rnd)
    if i == rnd:
        numofrounds = n//rnd
        # print(numofrounds)
        nik *= numofrounds
        pol *= numofrounds
        break
        #print(a[ai%alen], b[bi%blen])
    if a[ai] == b[bi]: pass
    elif (a[ai] == 'R' and b[bi] == 'S') or (a[ai] == 'S'
        and b[bi] == 'P') or (a[ai] == 'P' and b[bi] == 'R'):
        pol += 1
    else: nik += 1
    ai = (ai+1)%alen
    bi = (bi+1)%blen
if n%rnd != 0 and numofrounds != 0:
    n -= rnd*numofrounds
    ai = 0
    bi = 0
    for i in range(n):
        if a[ai] == b[bi]: pass
        elif (a[ai] == 'R' and b[bi] == 'S') or (a[ai] == 'S'
        and b[bi] == 'P') or (a[ai] == 'P' and b[bi] == 'R'):
            pol += 1
        else: nik += 1
        ai = (ai+1)%alen
        bi = (bi+1)%blen
print(nik, pol)   
```