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
2016-12-08 12:38:29
LOL!!! its as easy as it looks
2016-11-27 03:28:21
Easy, analyze the given examples.
A/C in one go using O(1) memory and 0s in C++ without recursion.
Sets and maps will work great,I solved this using Floyd's.
2016-11-04 07:43:38 E Naveen Kumar
Please analyse carefully. Simple
AC in a Go.....
2016-10-29 08:00:03
Think as simple as you can as even for the largest 10 digit number.

Last edit: 2016-10-29 08:00:37
2016-10-28 13:49:33
Ac after analyzing the pattern for different numbers!!!

Last edit: 2016-10-28 13:50:04
2016-10-26 22:07:51
try map.AC in first go...
2016-09-03 13:56:39 Vaporeon
Easy one using hashing.
2016-08-19 21:58:50
no memoization just write main function for 1 file
2016-08-13 23:39:41
trick is hidden in the e.g . 204
2016-07-26 13:28:11
AC in one go. Absolutely simple logic. NO memoization needed. The solution is as simple as it looks like.
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