eolymp
Problems

Good Versus Evil

Good Versus Evil

Middle Earth is about to go to war. The forces of good will have many battles with the forces of evil. Different races will certainly be involved. Each race has a certain 'worth' when battling against others. On the side of good we have the following races, with their associated worth:

Hobbits - 1

Men - 2

Elves - 3

Dwarves - 3

Eagles - 4

Wizards - 10

On the side of evil we have:

Orcs - 1

Men - 2

Wargs - 2

Goblins - 2

Uruk Hai - 3

Trolls - 5

Wizards - 10

Although weather, location, supplies and valor play a part in any battle, if you add up the worth of the side of good and compare it with the worth of the side of evil, the side with the larger worth will tend to win.

Thus, given the count of each of the races on the side of good, followed by the count of each of the races on the side of evil, determine which side wins.

Input

The first line contains an integer greater than 0 signifying the number of battles to process. Information for each battle will consist of two lines of data as follows.

First, there will be a line containing the count of each race on the side of good. Each entry will be separated by a single space. The values will be ordered as follows: Hobbits, Men, Elves, Dwarves, Eagles, Wizards.

The next line will contain the count of each race on the side of evil in the following order: Orcs, Men, Wargs, Goblins, Uruk Hai, Trolls, Wizards.

All values are non-negative integers. The resulting sum of the worth for each side will not exceed the limit of a 32-bit integer.

Output

For each battle, print "Battle" followed by a single space, followed by the battle number starting at 1, followed by a ":", followed by a single space. Then print "**Good triumphs over Evil**" if good wins. Print "**Evil eradicates all trace of Good**" if evil wins. If there is a tie, then print "**No victor on this battle field**".

Time limit 1 second
Memory limit 64 MiB
Input example #1
3
1 1 1 1 1 1
1 1 1 1 1 1 1
0 0 0 0 0 10
0 1 1 1 1 0 0
1 0 0 0 0 0
1 0 0 0 0 0 0
Output example #1
Battle 1: Evil eradicates all trace of Good
Battle 2: Good triumphs over Evil
Battle 3: No victor on this battle field
Source 2012 ACM North America - Pacific Northwest, November 3, Problem A