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.
#include <bits/stdc++.h>
int getcd(int a, int b) {
  if (a % b) return getcd(b, a % b);
  return b;
}
int get(char a, char b) {
  if (a ^ b) {
    switch (a) {
      case 'R':
        return b == 'S' ? 1 : -1;
      case 'S':
        return b == 'P' ? 1 : -1;
      case 'P':
        return b == 'R' ? 1 : -1;
    }
  }
  return 0;
}
int main() {
  int n;
  char sa[1001], sb[1001];
  int la, lb;
  int len;
  int i;
  int ra, rb, resa, resb;
  int res;
  while (scanf("%d", &n) != EOF) {
    res = ra = rb = resa = resb = 0;
    scanf("%s%s", sa, sb);
    la = strlen(sa);
    lb = strlen(sb);
    len = la / getcd(la, lb) * lb;
    res = n % len;
    for (i = 0; i < res; ++i) {
      switch (get(sa[i % la], sb[i % lb])) {
        case 1:
          ++resa;
          break;
        case -1:
          ++resb;
          break;
      }
    }
    ra = resa;
    rb = resb;
    for (i = res; i < len; ++i) {
      switch (get(sa[i % la], sb[i % lb])) {
        case 1:
          ++ra;
          break;
        case -1:
          ++rb;
          break;
      }
    }
    printf("%d %d\n", rb * (n / len) + resb, ra * (n / len) + resa);
  }
  return 0;
}
