### Day 2 Question 1

# High Tide

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Input file: probd.in

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Output file: probd.out

A planet has *n* moons revolving about it in constant clockwise coplanar circular orbits. How often do **all** the moons appear directly overhead as viewed from some point on the planet? We will call such a situation a 'vertical alignment'.

Your input consists of a number of sets of lines; each set consists of an integer *n*, indicating the number of moons, followed by *n* distinct positive integers, one per line, indicating the exact period of revolution for each moon, in days. (Thus there are *n*+1 lines of data for each set with the first line containing *n*.) The last line contains only a zero.

For each input set, except the last, generate a line of output indicating the interval in days, to two decimal places, between consecutive vertical alignments.

### Sample Input

2
20
30
3
20
30
40
2
10
3
0

### Sample Output

60.00
120.00
4.29