...When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth.

You are given an unknown number within the range of 1 to 100, inclusive.
Your task is to **guess what the number is by performing a series of guesses**.

Your solution will need to guess the number by submitting an **integer divisor** ranging from 2 to 10,
and the **number you guessed**.
At each attempt you will get information as a list of tuples. Each tuple contains the remainder result along with
your previous divisor.

You should find the number within 8 guesses. We will give you a little extra info on your first attempt... *Use
it wisely young grasshopper*...

Consider the following example:

Attempt |
Divisor |
Guess |
Submit |
Information |
Remark |

1 | 2 | 99 | (2,99) | (1,5),(1,2) | You try a divisor of 2 and try your luck with 99; however, you've got information as a list of tuples, returning the remainder of your previous divisor along with your previous divisor. (that means, you still need to guess) |

2 | 3 | 91 | (3,91) | (1,5),(1,2),(2,3) | Your solution may suggest 91 because it passed with the information data. Is it? ( 91%5=1; 91%2=1 )Again, you've still got no response. Guess again. |

3 | 6 | 41 | (6,41) | (1,5),(1,2),(2,3),(5,6) | Your solution might suggest 41 because it passed with the information data. ( 41%5=1; 41%2=1; 41%3=2 ) Again, you've still got no response. |

4 | 4 | 71 | (4,71) | (1,5),(1,2),(2,3),(5,6),(3,4) | Your solution may suggest 71 because it passed with the information data. ( 71%5=1; 71%2=1; 71%3=2; 71%6=5 ) Now there are only 4 remaining attempts left. |

5 | and, so on... | ||||

6 | |||||

7 | |||||

8 |

Attempt |
Divisor |
Guess |
Submit |
Response |

1 | 2 | 99 | (2,99) | (1,5),(1,2) |

Remark #1:You try a divisor of 2 and try your luck with 99; however, you've got a response of a list of tuples, returning the remainder of your previous divisor and your previous divisor. ( that means you still need to guess ) |
||||

2 | 3 | 91 | (3,91) | (1,5),(1,2),(2,3) |

Remark #2:Your solution suggests 91 because it passed with the response data, isn't it? ( 91%5=1; 91%2=1 ) Again, you've still got a response. Next guess, then. |
||||

3 | 6 | 41 | (6,41) | (1,5),(1,2),(2,3),(5,6) |

Remark #3:Your solution suggests 41 because it passed with the response data. ( 41%5=1; 41%2=1; 41%3=2 ) Again, you've still got a response. |
||||

4 | 4 | 71 | (4,71) | (1,5),(1,2),(2,3),(5,6),(3,4) |

Remark #4:Your solution suggests 71 because it passed with the response data. ( 71%5=1; 71%2=1; 71%3=2; 71%6=5 ) Again, you've still got a response. |
||||

5 | and, so on... | |||

6 | ||||

7 | ||||

8 |

You get the idea...

**Input: ** Information about the previous attempt. A list of tuples. Each tuple contains its remainder
and the previous divisor.

**Output: ** A list of integer divisors and your best guess. A list of two integers.

**Example:**

checkio([(1,5)]) # the number has a remainder 1 checkio([(1,5),(1,2)]) # the number has a remainder 1 checkio([(1,5),(1,2),(2,3)]) # the number has a remainder 2 checkio([(1,5),(1,2),(2,3),(5,6)]) # the number has a remainder 5 checkio([(1,5),(1,2),(2,3),(5,6),(3,4)]) # the number has a remainder 3

**How it is used:**
This is a classical prediction and decision problem.
You have some indirect information and should to get hidden by it data.
The skills that go into this problem could help you create a sports bracket for the office pool.

**Precondition: **

0 < number ≤ 100