1 s   128 MB

## Description

This time, instead of solving an easy problem with a known solution, you will be in charge in solving an old problem with a solution which was unknown to this date. The old question is whether the egg or the chicken came first. This question has been very difficult to answer over the ages, but a chance has finally come: It is said that a new oracle has appeared which knows everything.

You are still suspiscious that the explanation given by the oracle is another lie. Given ints neggCountlieCount and liarCount, find out if scenarios exist such that "The egg" or "The chicken" is the correct answer. If there exist scenarios such that either answer is correct, print 'Ambiguous" (quotes for clarity). If only one answer has a possible scenario, print "The egg" or "The chicken" (quotes for clarity) depending on the answer. If neither of the answers has a possible scenario, print "The oracle is a lie".

## Input

The first line of the input gives the number of test cases, T (1 <= T <= 200).

Each test case is represented by four integers n, eggCount, lieCount, liarCount, in one line. N will be between 1 and 1000000, inclusive, and latter three integers will be between 0 and n, inclusive.

## Output

For each test case, print the result as explained in the problem statement, in one line.

### Sample Output

4
10 10 0 0
60 40 0 30
60 20 5 25
1000 500 250 250
The egg
The oracle is a lie
The chicken
Ambiguous