CF173A.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 = (_a_1, _a_2, ..., a__m), 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: _a_1, _a_2, ..., a__m, _a_1, _a_2, ..., a__m, _a_1, ... and so on. Polycarpus had a similar strategy, only he had his own sequence of items B = (_b_1, _b_2, ..., b__k).

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.

尼基福罗斯和波利卡尔普斯玩“石头剪刀布”游戏。输的一方会被轻轻捏一下（不会太疼）！

我们来回顾一下这个游戏的规则：石头剪刀布由两名玩家进行。每一轮中，双方各自独立地选择三种手势之一：石头、剪刀或布，并用手势表示出来。胜负判定规则如下：石头胜剪刀，剪刀胜布，布胜石头；若双方出相同的手势，则该轮为平局。

尼基福罗斯和波利卡尔普斯共进行了 $ n $ 轮游戏。每一轮中，获胜者会友好地捏一下失败者，失败者身上因此出现一个崭新的红色小点；若该轮为平局，则双方什么也不做，直接进入下一轮。

尼基福罗斯事先制定了一套策略：游戏开始前，他选定一个长度为 $ m $ 的手势序列 $ A = (a_1, a_2, \dots, a_m) $，然后按循环方式依次展示该序列中的手势，即从第一个手势开始，依次展示 $ a_1, a_2, \dots, a_m $，接着再次从 $ a_1 $ 开始，如此反复：$ a_1, a_2, \dots, a_m, a_1, a_2, \dots, a_m, a_1, \dots $。波利卡尔普斯也采用类似策略，但他有自己的手势序列 $ B = (b_1, b_2, \dots, b_k) $。

请计算在进行完 $ n $ 轮游戏后，两名玩家身上各自有多少个红色小点。初始时，两人身上均无红点。

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.

第一行包含一个整数 $n$（$1 ≤ n ≤ 2·10^9$）—— 表示游戏的轮数。

第二行包含字符串形式的序列 $A$，长度为 $m$；第三行包含字符串形式的序列 $B$，长度为 $k$（$1 ≤ m, k ≤ 1000$）。所给字符串仅包含字符 "R"、"S" 和 "P"。其中，"R" 表示石头（Rock），"S" 表示剪刀（Scissors），"P" 表示布（Paper）。

Print two space-separated integers: the numbers of red spots Nikephoros and Polycarpus have.

输出两个用空格分隔的整数：尼基福罗斯和波利卡普斯各自拥有的红色斑点数量。

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.

在第一个样例中，游戏过程如下：

• R - R：平局。
• P - S：尼基福罗斯输。
• S - P：波利卡普斯输。
• R - P：尼基福罗斯输。
• P - R：波利卡普斯输。
• S - S：平局。
• R - P：尼基福罗斯输。

因此，尼基福罗斯总共输了 3 次（对应 3 个红点），而波利卡普斯仅输了 2 次。