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
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.

sonali9696: 2016-06-07 18:52:14

Concentrate on all possible single digits, you will know which two are important. Happy coding :)

nonushikhar: 2016-03-23 20:59:27

do math for n=10 or 15 and u'll get it

akshayvenkat: 2016-02-11 15:05:52

please don't complicate it much. its actually a very simple problem. i ll give you a tip. the count variable has a certain limiting value. Beyond that, the answer will always be -1. With this, you should be able to proceed.. And write the code for 1 INPUT alone. "number of input files is 32 " doesn't concern the problem in any way.. Good luck (y)

Last edit: 2016-02-11 15:06:11
aditya1997: 2016-02-09 00:14:30

set.....the key to AC :)

Aqib Ahmed J: 2016-01-31 07:48:11

Tick mark in one go :)

Parikshith Rai: 2016-01-23 07:39:30

got 3 nzecs only because i thought that there are 32 test cases.
haha..well,now I'm embarrassed :D


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