Problem: Btoh yuo adn yuor roomatme lhoate wianshg disehs, btu stlil sdmoeboy msut peorrfm tihs cohre dialy. Oen dya yuo decdie to idourtcne smoe syestm. Yuor rmmotaoe sstgegus teh fooniwllg dael. Yuo argee on tow arayrs of ientgres M adn R, nmebur upmicnog dyas (induiclng teh cunrret oen) wtih sicsescuve irnegets (teh ceurrnt dya is zreo), adn yuo wsah teh diehss on dya D if adn olny if terhe etsixs an iednx i scuh taht D mod M[i] = R[i], otwsehrie yuor rmootmae deos it. Yuo lkie teh cncepot, btu yuor rmotaome's cuinnng simle meaks yuo ssecupt sthnoemig, so yuo itennd to vefriy teh fnerisas of teh aemnrgeet.

Yuo aer geivn ayarrs M adn R. Cuaclatle teh pceanregte of dyas on wchih yuo edn up dnoig teh wisahng. Amsuse taht yuo hvae iiiftlneny mnay dyas aehad of yuo. 

Input

The first line of input contains a single integer N (1 ≤ N ≤ 16).

The second and third lines of input contain N integers each, all between 0 and 16, inclusive, and represent arrays M and R, respectively. All M[i] are positive, for each i R[i] < M[i].

Output

Output a single real number. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 4.

Examples

Input

1
2
0


Output

0.500000


Input

2
2 3
1 0


Output

0.666667

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

/*

Both you and your roommate loathe washing dishes, but still somebody must
perform this chore daily. One day you decide to ? some system. Your roommate
suggests the following deal. You agree on two arrays of integers M and R,
number upcoming days (including the current one) with successive integers (the
current day is zero), and you wash the dishes on day D if and only if there
exists an index such that D mod M[i] = R[i], otherwise your roommate does it.
You like the concept, but your roommate's cunning smile makes you suspect
something, so you intend to verify the ? of the agreement.

You are given arrays M and R. Calculate the percentage of days on which you
end up doing the washing. Assume that you have infinitely many days ahead of
you.
 
 */

public class CF656B {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine());
		int[] mm = new int[n];
		for (int i = 0; i < n; i++)
			mm[i] = Integer.parseInt(st.nextToken());
		st = new StringTokenizer(br.readLine());
		int[] rr = new int[n];
		for (int i = 0; i < n; i++)
			rr[i] = Integer.parseInt(st.nextToken());
		int cnt = 0, max = 100000;
		for (int d = 0; d < max; d++) {
			boolean yes = false;
			for (int i = 0; i < n; i++)
				if (d % mm[i] == rr[i]) {
					yes = true;
					break;
				}
			if (yes)
				cnt++;
		}
		System.out.println((double) cnt / max);
	}
}