An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value. For instance, 2, 5, 8, 11, 14,... and 7, 3, –1, –5,... are arithmetic, since you add 3 and subtract 4, respectively, at each step. A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... and 81, 27, 9, 3, 1, 1/3,... are geometric, since you multiply by 2 and divide by 3, respectively, at each step.

The number added (or subtracted) at each stage of an arithmetic sequence is called the "common difference"

 The number multiplied (or divided) at each stage of a geometric sequence is called the "common ratio"

Given an integer N you will take N numbers determine whether they form  an Arithmetic sequence (and/or) Geometric sequence or not and print their common differnece and common ration 

Print -1 if the sequence doesn't form Arithmetic sequence

The same for Geometric sequence

Input

N : number of following integers .. N>1

N integers all integers are from -100 to 100 inclusive

Output

Four lines

the first line contains 1 if the sequence form an arithmetic sequence , 0 if not

the second line contains the common difference , -1 if not forming arithmetic sequence

the first line contains 1 if the sequence form an geometric sequence , 0 if not

the second line contains the common ratio , -1 if not forming geometric sequence

Example

Input:
5

1 2 3 4 5

Output:
1 1

0 -1

Input:

5

16 8 4 2 1

Output:

0 -1

1 2

Input:

5

5 4 3 2 1

Output:

1 1

0 -1