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
neel_butani: 2020-06-25 07:44:31

try different test case from 1 to 10 , you will notice a pattern and that's it !!ac

navdeep1469: 2020-06-18 13:52:46

Do not complicate things. Solution is hidden in the test case itself.

dante_part_2: 2020-04-24 16:09:49

How can we pre-calculate values??

abhishek_251: 2020-04-19 20:55:57

i hate brute force kinda questions

raviteja_30: 2019-09-11 18:51:28

50th one.......! wow , feeling happy.

xxxadityaxxx: 2019-09-02 19:57:27

used HashSet

sanket17: 2019-07-08 11:35:58

Dont think two much
Use Brute Force it will AC

shubham97361: 2019-06-21 13:20:54

Think simple.

hetp111: 2019-05-28 08:03:05

Ezzz

iamabhishiek: 2019-04-15 10:29:50

memorization works


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