Cookie Exchanges

Takahashi, Aoki and Snuke love cookies. They have A, B and C cookies, respectively. Now, they will exchange those cookies by repeating the action below:

• Each person simultaneously divides his cookies in half and gives one half to each of the other two persons.

This action will be repeated until there is a person with odd number of cookies in hand.

How many times will they repeat this action? Note that the answer may not be finite.

Constraints

• 1 ≤ A,B,C ≤ 10^9

Input

Input is given from Standard Input in the following format:

A B C

Output

Print the number of times the action will be performed by the three people, if this number is finite. If it is infinite, print -1 instead.

Examples

Input

4 12 20

Output

3

Input

14 14 14

Output

-1

Input

454 414 444

Output

1

inputFormat

Input

Input is given from Standard Input in the following format:

A B C

outputFormat

Output

Print the number of times the action will be performed by the three people, if this number is finite. If it is infinite, print -1 instead.

Examples

Input

4 12 20

Output

3

Input

14 14 14

Output

-1

Input

454 414 444

Output

1

样例

14 14 14

-1