## Goal

A polydivisible number (or magic number) is a number with digits abcde... that has the following properties :

- Its first digit a is not 0.

- The number formed by its first two digits ab is a multiple of 2.

- The number formed by its first three digits abc is a multiple of 3.

- The number formed by its first four digits abcd is a multiple of 4.

- etc...

For example, 567 is polydivisible because :

- 5 is divisible by 1

- 56 is divisible by 2

- 567 is divisible by 3

Your program will have to determine in which bases the input number may be, knowing that it is polydivisible in base 10
Input

One line containing the number consisting of pairs of numbers separated by spaces

01 02 03 => 123 in base 10

01 02 03 => 123 in base 16 => 291 in base 10

01 10 02 => 1A2 in base 16 => 418 in base 10

Output

The values of the bases by numeric order

Constraints

2 ≤ `base` ≤36

number of digits < 18

Example

Output

5
6
8
9
11
12
14
15
16
20
24
28
29
35