CLTZ - Collatz

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Let N be a positive integer, Consider the following recurrence: f(1) = N and f(K) = (0.5 + 2.5 * (f(K-1) mod 2)) * f(K-1) + (f(K-1) mod 2) if K>1. For a given N you have to compute the smallest L for which f(L)=1 (such an L always exists for N's in the input).

Input

Each line contains a positive integer N in decimal notation. You can be sure that N and all intermediate results are not bigger than 10^1888. Input terminated by EOF.

Output

For each number N in the input print one line with the value of L in decimal notation.

Example

Input:
1
2
321
1111111111111
111111111111111111111111111111111111111111111111111111111111
Output:
1
2
25
261
1296

hide comments
vijayphoenix: 2018-12-05 16:46:08

Use python or java....it will make ur life easy

Punit Singh Koura: 2013-06-22 20:04:36

can someone suggest some tricky test cases. I am getting wrong answer but i dont know why.

nani: 2012-07-14 17:00:57

Last edit: 2013-07-10 16:51:37
Muhammad Ridowan: 2011-09-06 21:55:16

Its from unproven Collatz conjecture. So probably there is no O(1) type solution.

刘启鹏: 2011-09-06 21:55:16

i guess that brute force algorithm is enough for the problem.


Added by:czylabsonasa
Date:2005-04-25
Time limit:1.983s
Source limit:18000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Folklore