TIP2  Totient in permutation (medium)
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 < 10^2 1 < M < 10^12
Code size limit is 10kB ; the upper bound was set at 10^12 to make a (C/pascal/...)solution easier to write. Constraints allow Python3 users to get AC under 1.86s (with a suboptimal solution). (Edit 20170211, after compiler updates)
If if you get TLE, you should try first TIP1.
If it's too easy for you TIP3 is made for you ;)
hide comments
[Rampage] Blue.Mary:
20160607 05:13:43
I agree with @mikhaelkh. My program works with uniformly random input. If the input is loguniform random ones, it has a large probability to get TLE.


[Lakshman]:
20150706 10:38:34
Thanks @The next big thing for pointing out the mistake. 

[Lakshman]:
20150703 05:30:22
@Francky Can you please check My code I am getting WA, will this approach work? or I have to find some other method.


Michael Kharitonov:
20130311 18:33:18
Game, set and match.


Michael Kharitonov:
20130311 11:10:10
I think tests are weak. For example no tests below 1e7. I'd use loguniform distribution plus some tricky tests.

Added by:  Francky 
Date:  20130106 
Time limit:  3s 
Source limit:  10000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  TIP1 extension 