Practice Number theory and Mathematics with the exercise "Mask-Matching"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Number theory
Mathematics
Combinatorics

Statement

Goal

You are given a positive integer called mask in hexadecimal notation, which is less than 2^28. Your task is to find up to 15 integers that match the condition:

(mask & n) == n

where n is a positive integer. These integers are called mask-matching integers.

Output the mask-matching integers in decimal form, starting from the smallest. If there are more than 15 integers that match, output the first 13 smallest numbers, followed by ,..., and the last 2 largest numbers.

Input

Line 1: A single positive integer mask in hexadecimal notation

Output

Line 1: A comma-separated list of up to 15 mask-matching integers in decimal.

Constraints

1 ≤ mask ≤ 0x3FFF_FFFF_FFFF_FFFF (i.e. 2^62 - 1)

Example

Input

Output

2,4,6,8,10,12,14

Solve it

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