HPYNOS - Happy Numbers I

The process of “breaking” an integer is defined as summing the squares of its digits. For example, the result of breaking the integer 125 is (12 + 22 + 52) = 30. An integer N is happy if after “breaking” it repeatedly the result reaches 1. If the result never reaches 1 no matter how many times the “breaking” is repeated, then N is not a happy number.

TASK

Write a program that given an integer N, determines whether it is a happy number or not.

CONSTRAINTS

2 ≤ N ≤ 2,147,483,647

Input

A single line containing a single integer N.

Output

A single line containing a single integer T which is the number of times the process had to be done to determine that N is happy, or -1 if N is not happy.

Example

Input:
19

Output:
4
1) 19  : 12 + 92 = 82
2) 82  : 82 + 22 = 68
3) 68  : 62 + 82 = 100
4) 100 : 12 + 02 + 02 = 1

The solution is 4 because we discovered that the integer 19 is happy after we repeated the process 4 times.

Input:
204

Output:
-1
204 –> 20 –> 4 –> 16 –> 37 –> 58 –> 89 –> 145 –> 42 –> 20 –> 4 –> 16 –> 37 –> 58 –> 89 –> 145 ……

204 is not a happy number because after breaking it several times the results start repeating so we can deduce that if we continue breaking it, the result will never reach 1.

Number of input files is 32.

Don't use pre-calculated values (Don't Cheat)!!!


Added by:Rofael Emil
Date:2010-11-03
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Egyptian Olympiad in Informatics ( EOI ) 2009, August 14 - 21, Cairo

hide comments
2018-04-02 18:20:20
Bill got AC in 1 go.
Bill didn't write "AC in 1 go" in comment section.
He knew it was an easy question and there is no meaning of show off.
Bill is smart.
Be like Bill.
2018-03-20 13:51:21
AC in one go without using cycle detection!
2018-02-23 15:41:12
AC in one go!!!
thanx to @jayeshd his comment was crucial .....without using any cycle detection...
2018-02-06 17:19:55
@jayeshd thanks alot found another way without using Floyd's cycle.
2018-01-12 00:24:08
Getting WA after more than 20 test cases. Could someone suggest some conditions that I might be missing? Solution id is 20968234.
2018-01-01 17:52:12
Learnt to use set, what set insert returns and how to receive and compare whether value was inserted in addition to operating with digits
2017-11-30 12:36:09
AC in first time...
2017-11-12 05:41:00
ac in second go minor mistake

Last edit: 2017-11-12 11:33:21
2017-10-16 10:30:06
AC in one go!!solved in less than 10 minutes...no thinking required
2017-09-17 14:14:42
Take 3 hr but finally AC !! huh..
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