TIP1  Totient in permutation (easy)
In number theory, Euler's totient (or PHI function), is an arithmetic function that counts the number of positive integers less than or equal to a positive integer N that are relatively prime to this number N.
That is, if N is a positive integer, then PHI(N) is the number of integers K for which GCD(N, K) = 1 and 1 ≤ K ≤ N. We denote GCD the Greatest Common Divisor. For example, we have PHI(9)=6.
Interestingly, PHI(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
Input
The input begins with the number T of test cases in a single line.
In each of the next T lines there are an integer M.
Output
For each given M, you have to print on a single line the value of N, for which 1 < N < M, PHI(N) is a permutation of N and the ratio N/PHI(N) produces a minimum. If there's several answers output the greatest, or if need, "No solution." without quotes.
Leading zeros are not allowed for integers greater than 0.
Example
Input: 3 22 222 2222 Output: 21 63 291
Explanations :
For the first case, in the range ]1..22[, the lonely number n for witch phi(n) is in permutations(n) is 21, (we have phi(21)=12). So the answer is obviously 21.
For the second case, in the range ]1..222[, there's two numbers n for witch phi(n) is in permutations(n), we have phi(21)=12 and phi(63)=36. But as 63/36 is equal to 21/12, we're taking the greater : 63.
For the third case, in the range ]1..2222[, there's four numbers n for witch phi(n) is in permutations(n), phi(21)=12, phi(63)=36, phi(291)=192 and phi(502)=250. Within those solutions 291/192 is the minimum, we output 291.
Constraints
1 < T < 10^5 1 < M < 10^7
Code size limit is 10kB ; less than 500B of python3 code can get AC under 2s.
After that you may try TIP2.
@Speed addicts : my C code ran in 0.02s, and my fastest python3.2 code ran in 1.21s, (0.90s in py2.7)
Edit 20170211, after compiler updates. My old C code ends in 0.00s, my old Python code ends in 0.05s !!!
hide comments
priyanshu_pg:
20190109 08:56:13
Thanks @Francky.


priyanshu_pg:
20190108 12:25:41
@Francky Can you please check my code. I am getting right answers for every test case on Spoj Toolkit.


Francky:
20170212 15:36:17
Congratulations to Tjandra for being the lonely (for now) Python solver. Here, there's a little challenge. 

DHEERAJ KUMAR:
20160320 22:47:29
@Francky do i have WA for many inputs? submission id 16561400 

.:frUstrAteD:.:
20151003 21:50:00
@Francky Can you please check my code is getting WA


Maroof:
20150712 13:30:47
@FRANCKY do I have a lot of WAs in my last submission?


[Lakshman]:
20150702 05:36:33
AC now. A small bug and unlimited WA.


[Lakshman]:
20150130 07:53:48
@Francky Can you please check my code getting WA, I have checked several test cases with my brute force code and getting correct answer.


Harry Mathis:
20141030 10:17:54
I get always a runtime error (NZEC) with my java code, but i have no idee what i'm doing wrong? Is it possible, that the input numbers are Strings? I expect integers.


Flago:
20140519 14:39:22
"No solution" != "No solution."

Added by:  Francky 
Date:  20130106 
Time limit:  1.399s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Extension of Project Euler n°### 