The Foxen's Treasure

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Points: 5
Time limit: 4.5s
Memory limit: 64M

Author:
Problem type
University of Toronto ACM-ICPC Tryouts 2012

There are Foxen guarding a certain valuable treasure, which you'd love to get your hands on. The problem is, the Foxen certainly aren't about to allow that - at least, not while they're awake.

Fortunately, through careful observation, you've seen that each Fox has a regular sleep cycle. In particular, the th Fox stays awake for hours, then sleeps for hours, repeating this pattern indefinitely . At the start of your treasure-nabbing attempt, the th Fox is exactly hours into its cycle.

There are scenarios as described above. For each one, you'd like to determine how soon all of the Foxen will be simultaneously asleep, allowing you to grab their treasure, or if this will simply never happen.

Input Specification

Line 1: 1 integer,
For each scenario:
Line 1: 1 integer,
Next lines: 3 integers, , , and , for

Output Specification

For each scenario:
Line 1: 1 integer, the minimum number of hours after the start to wait until all of the Foxen are asleep during the same hour. If this will never happen, output Foxen are too powerful instead.

Sample Input

2
2
2 1 2
2 2 1
3
1 1 0
1 1 0
1 1 1

Sample Output

6
Foxen are too powerful

Explanation of Sample

In scenario 1, the following table illustrates the Foxen's sleeping cycles (with A representing being awake, S representing sleep, and a bold letter representing the start of a sleep cycle):

Hour Fox 1 Fox 2
0 S A
1 A S
2 A S
3 S A
4 A A
5 A S
6 S S

As can be seen, the first hour during which both Foxen are asleep is 6 hours after the start.

In scenario 2, the first 2 Foxen are always awake and asleep at the same times. However, the third Fox's schedule is exactly flipped, which means that it will never be asleep at the same time as the others.