HPYNOSII - Happy Numbers II

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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 T (number of test cases) and T integers, determines for each number whether it is a happy number or not.

CONSTRAINTS

1 ≤ T ≤ 1,080,000

2 ≤ N ≤ 2,147,483,647 (number for determining whether it is happy or not)

Input

The first line contains an integer T.

Next 1...T lines contain an integer N for detemining whether it is happy or not.

Output

T lines containing a single integer N 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:
2
19
204

Output:
4
-1
1) 19  : 12 + 92 = 82
2) 82  : 82 + 22 = 68
3) 68  : 62 + 82 = 100
4) 100 : 12 + 02 + 02 = 1

The solution for 19 is 4 because we discovered that the integer 19 is happy after we repeated the process 4 times.

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.


hide comments
nadstratosfer: 2018-04-08 03:37:02

Optimized (!) O(1) in PyPy gets 0.50 in the tutorial version, hence TLE here. Don't waste your time on this garbage, use INTEST for IO optimizations instead.

karthik1997: 2018-01-01 21:05:50

Man , used floyd cycle detection and all i could do is to solve it in 0.10s. Cant get below it . :(

coder_hsnake: 2016-08-30 13:12:45

wow same solution of happy number got me AC in one go!!!!! and this is no I/O race scanf and printf works fine

Piyush Kumar: 2016-06-24 20:05:35

So the difference between this and HYPNOS is just IO. :(

shantanu tripathi: 2015-08-29 21:25:16

fread_unlocked will work... very strict i/o...rest is precomputation :)

Ankit: 2015-08-18 16:25:51

use getchar_unlocked :)

:.Mohib.:: 2015-08-01 17:42:54

Nice..!!

Aditya Kumar: 2015-06-29 11:12:26

finally AC.....
precomputation + O(n) + gets

Last edit: 2015-06-29 11:19:15
ASHUTOSH DWIVEDI: 2015-06-25 23:11:36

hell of a problem
ruined my day

Vipul Srivastava: 2015-06-20 14:00:45

My 2 different solutions one giving 1 for 1000000 and the other giving 2 for the same get AC.


Added by:Rofael Emil
Date:2010-11-05
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:(modified) Egyptian Olympiad in Informatics ( EOI ) 2009, August 14 - 21, Cairo