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
sinersnvrsleep: 2017-11-12 05:41:00

ac in second go minor mistake

Last edit: 2017-11-12 11:33:21
kush_pathak01: 2017-10-16 10:30:06

AC in one go!!solved in less than 10 minutes...no thinking required

deepak097: 2017-09-17 14:14:42

Take 3 hr but finally AC !! huh..

jayeshd: 2017-09-08 20:42:23

The theoretical maxima of a loop length will be very less and can be a good problem in itself (given N ≤ 2,147,483,647). The max sum of squares can be 1^2 + 81*9 = 730, in the next step the number would become even lesser. So we can be pretty sure that even if there is a loop its length will be in 3 digits. Though actually, the highest loop size is just 20 given N ≤ 2,147,483,647.

Last edit: 2017-09-08 20:42:55
addy1397: 2017-07-24 10:56:17

7 sucks ...right!

ramesh_961: 2017-06-04 14:04:09

can Learn Floyd's cycle detection!! Easy!!

akababa: 2017-04-26 07:25:00

How would you even use pre-calculated valuess... lol

visu27: 2017-03-23 10:21:21

easy one AC in one go

stark_attack: 2017-02-23 11:34:14

very easy , with just two loops .AC in first go .....

cake_is_a_lie: 2017-02-11 00:37:59

Lots of ways to solve this, but for me the thought pattern was "if only I could easily find a bound on the number of iterations it might take to reach 1"...


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