### Problem Statement

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 n, eggCount, lieCount 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, return "Ambiguous" (quotes for clarity). If only one answer has a possible scenario, return "The egg" or "The chicken" (quotes for clarity) depending on the answer. If neither of the answers has a possible scenario, return "The oracle is a lie".

### Definition

 Class: ChickenOracle Method: theTruth Parameters: int, int, int, int Returns: String Method signature: String theTruth(int n, int eggCount, int lieCount, int liarCount) (be sure your method is public)

### Constraints

-n will be between 1 and 1000000, inclusive.
-eggCount, lieCount and liarCount will each be between 0 and n, inclusive.

### Examples

0)

 `10` `10` `0` `0`
`Returns: "The egg"`
 In this case, every person has answered correctly.
1)

 `60` `40` `0` `30`
`Returns: "The oracle is a lie"`
 According to the oracle, it has told the correct answer to all 60 people and then 30 of them lied to you. However, it contradicts the fact that 40 people have told you one answer and 20 people have told another one.
2)

 `60` `20` `5` `25`
`Returns: "The chicken"`
3)

 `1000` `500` `250` `250`
`Returns: "Ambiguous"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=11004

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14234&pm=11004

vexorian

#### Testers:

PabloGilberto , ivan_metelsky , Chmel_Tolstiy

#### Problem categories:

Simple Math, Simple Search, Iteration