说明

DotA(Defence of the Ancients) is very popular in Zhejiang University.Now a new hero appears in DotA.This hero has a miraculous skill.If the target's HP n is an even number,then it will be cut in half after skill-using.Otherwise the targe's HP will plus one after skill-using.Given a target's HP,we want to decrease the target's HP from n to 1 only with this new skill.

输入格式

The input consists of multiple test cases.Each case contain one line with an integer n(1<n≤1000000000).

输出格式

For each test case,output the target's HP's changing process on a single line.The HP values connect with '-' character.

样例

5
21

5-6-3-4-2-1
21-22-11-12-6-3-4-2-1