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 java.util.Scanner;

public class P173A_RockPaperScissors {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		long n = scanner.nextLong();
		String cycle1 = scanner.next();
		String cycle2 = scanner.next();
		scanner.close();

		int m = cycle1.length();
		int k = cycle2.length();
		int gcd = greatestCommonDivisor(m, k);
		int lcd = m / gcd * k;
		int mIndex = 0, kIndex = 0;
		int result = 0, resultM = 0, resultK = 0;

		if (n > lcd) {
			int mRound = k / gcd;

			while (mRound > 0) {
				result = round(cycle1.charAt(mIndex), cycle2.charAt(kIndex));

				if (result > 0) {
					resultM++;
				} else if (result < 0) {
					resultK++;
				}

				mIndex++;

				if (mIndex >= m) {
					mIndex = 0;
					mRound--;
				}

				kIndex++;

				if (kIndex >= k) {
					kIndex = 0;
				}
			}

			resultM *= n / lcd;
			resultK *= n / lcd;
			n %= lcd;
		}

		mIndex = 0;
		kIndex = 0;

		while (n > 0) {
			result = round(cycle1.charAt(mIndex), cycle2.charAt(kIndex));

			if (result > 0) {
				resultM++;
			} else if (result < 0) {
				resultK++;
			}

			mIndex++;

			if (mIndex >= m) {
				mIndex = 0;
			}

			kIndex++;

			if (kIndex >= k) {
				kIndex = 0;
			}

			n--;
		}

		System.out.println(resultK + " " + resultM);
	}

	private static int round(char ch1, char ch2) {
		if (ch1 == ch2) {
			return 0;
		}

		if (ch1 == 'R') {
			if (ch2 == 'S') {
				return 1;
			} else {
				return -1;
			}
		} else if (ch1 == 'P') {
			if (ch2 == 'R') {
				return 1;
			} else {
				return -1;
			}
		} else {
			if (ch2 == 'P') {
				return 1;
			} else {
				return -1;
			}
		}
	}

	private static int greatestCommonDivisor(int a, int b) {
		while (b != 0) {
			int temp = b;
			b = a % b;
			a = temp;
		}

		return a;
	}
}
