Problem Statement

We have $9K$ cards. For each $i = 1, 2, \dots, 9$, there are $K$ cards with $i$ written on it. We randomly shuffled these cards and handed out five cards - four face up and one face down - to each of Takahashi and Aoki. You are given a string $S$ representing the cards handed out to Takahashi and a string $T$ representing the cards handed out to Aoki. $S$ and $T$ are strings of five characters each. Each of the first four characters of each string is 1, 2, $\dots$, or 9, representing the number written on the face-up card. The last character of each string is #, representing that the card is face down. Let us define the score of a five-card hand as $\displaystyle \sum_{i=1}^9 i \times 10^{c_i}$, where $c_i$ is the number of cards with $i$ written on them. Takahashi wins when the score of Takahashi's hand is higher than that of Aoki's hand. Find the probability that Takahashi wins.

Constraints

• $2 ≤ K ≤ 10^5$
• $|S| = |T| = 5$
• The first through fourth characters of each of $S$ and $T$ are 1, 2, $\dots$, or 9.
• Each of the digit 1, 2, $\dots$, and 9 appears at most $K$ times in total in $S$ and $T$.
• The fifth character of each of $S$ and $T$ is #.

Input

Input is given from Standard Input in the following format:

K
S
T

Output

Print the probability that Takahashi wins, as a decimal. Your answer will be judged as correct when its absolute or relative error from our answer is at most $10^{-5}$.