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)!!!


hide comments
ankit1cool: 2016-08-19 21:58:50

no memoization just write main function for 1 file

manish3749: 2016-08-13 23:39:41

trick is hidden in the e.g . 204

deepika10: 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.

mattmurdock: 2016-07-17 16:27:10

Memoization.
AC One Go.

Guru Bala Dhinesh: 2016-07-07 15:44:09

Nobody asked for number of input files. cost me 1 NZEC.

wesolyfoton: 2016-06-27 03:04:24

Since when precalculating is a cheating?!?

roy_24: 2016-06-24 16:44:33

Dont complicate, can be done without using stl or memoization. Think easy.

baadshah_: 2016-06-23 13:50:44

use set STL

noob909: 2016-06-16 07:08:29

memoization :D ac in 1 go!

vineetpratik: 2016-06-13 19:13:09

Ac in one go , :D m happy.


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