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
Arif Awate: 2015-08-11 19:18:44

wow... for the first time i understood the significance of "do-while" loop!! though it cost me 1 WA..

NIKHIL KUMAR SINGH: 2015-08-07 11:57:48

The 32 test case thing costed me 1 WA .. @admin Please correct the problems statement it is misleading

detel: 2015-07-31 17:48:06

Its seems the input has been tremendously increased.
Earlier 0.00 in Python has changed to 0.25!!! :o

Last edit: 2015-07-31 17:48:27
Amartya Chaudhuri: 2015-07-19 19:07:06

Check out for single digit nos!!

mohit: 2015-07-06 16:29:28

hashing..

shravinson: 2015-07-06 16:23:55

when i was using memo ,it was giving WA..
without memo,run time error...
but after giving some conditions , it showed AC...
so be careful..

Aditya Kumar: 2015-06-29 10:09:25

silly mistake!! costed me some WA's

Sulabh Kumar: 2015-06-21 08:54:02

@Prasanna Patil :n can't be 1.it's given in constraints.

r0bo_dart: 2015-06-17 20:36:35

AC in first go.
Suggestions: Prepare your main for just one input.

Mayank Jethva: 2015-06-11 05:42:06

easy


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