## 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
 ankur314: 2018-06-21 10:23:26 when i took number of i/p files=32 i got WA but upto 32 files gives AC akshay_22: 2018-05-27 06:56:16 My time to really show off!!! xD AC in one go. Without any cycle detection code!! By far, the easiest solution !! :p syamphanindra: 2018-05-07 13:48:16 good problem .Tracing 32 nd case is tough for someone.If you give up search for 32nd test case in my blog. Last edit: 2018-05-07 13:48:30 abhinav__: 2018-04-02 18:20:20 Bill got AC in 1 go. Bill didn't write "AC in 1 go" in comment section. He knew it was an easy question and there is no meaning of show off. Bill is smart. Be like Bill. divya063: 2018-03-20 13:51:21 AC in one go without using cycle detection! ayusofayush: 2018-02-23 15:41:12 AC in one go!!! thanx to @jayeshd his comment was crucial .....without using any cycle detection... srjsunny: 2018-02-06 17:19:55 @jayeshd thanks alot found another way without using Floyd's cycle. vikramvarun: 2018-01-12 00:24:08 Getting WA after more than 20 test cases. Could someone suggest some conditions that I might be missing? Solution id is 20968234. amankumarjha: 2018-01-01 17:52:12 Learnt to use set, what set insert returns and how to receive and compare whether value was inserted in addition to operating with digits johansherlock: 2017-11-30 12:36:09 AC in first time...

 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