ARRANGE  Arranging Amplifiers
Scientists at the TIFR, Mumbai, are doing some cutting edge research on the Propagation of Signals. A young researcher comes up with a method of progressively amplifying signals, as they progress along a path. The method involves the placing of Amplifiers at regular distances along the line. Each amplifier is loaded with a number a(i), which is called its amplification factor. The method of amplification is simple: an amplifier which recieves a signal of strength X, and has Y loaded in it, results in a signal of strength Y^X [ Y to the power X]. In course of his research, the young scientist tries to find out, that given a set of n amplifiers loaded with a(0), a(1), a(2), ...., a(n1), which particular permutation of these amplifiers, when placed at successive nodes, with the initial node given a signal of strength 1, produces the strongest output signal.
this is better illustrated by the following example : 5 6 4
4^(5^(6^1)) is the strength of the strongest signal, which is generated by putting amplifier loaded with 6 in first place, 5 in second place and 4 in third place.
Given a list of integers specifying the set of amplifiers at hand, you must find out the order in which they must be placed, to get the highest signal strength. In case their exist multiple permutations with same output, you should print the one which has bigger amplifiers first.
Input
First line of input contains T, the number of test cases. For each test case first line contains a number ni, which is equal to the number of amplifiers available. Next line contains n integers, separated by spaces which denote the values with which the amplifiers are loaded.
Output
Output contains T lines, one for each test case. Each line contains ni integers, denoting the order in which the amplifiers should be kept such that the result is strongest.
Example
Input: 2 3 5 6 4 2 2 3 Output: 6 5 4 2 3
Constraints and Limits
T ≤ 20, Ni ≤ 10^5.
Each amplifier will be loaded with a positive integer p, 0 < p ≤ 10^9.
No two amplifier > 1 shall be loaded with the same integer.
hide comments
Ashot Minasyan :
20120105 09:38:59
@KickAss:


ink:
20120103 15:28:07
what will be the output for


sudipto das:
20100715 03:30:15
"No two amplifier > 1 shall be loaded with the same integer"means 1 can occur multiple times & other positive integers can occur only once......... 

:(){ :: & };::
20100414 08:00:59
For the test case:


Tasnim Khan:
20091218 20:38:12
2 1 = 1^2 = 1


Nikhil Garg:
20091218 12:53:00
Statement is not clear.

Added by:  Ajay Somani 
Date:  20080204 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  CodeCraft 08 Anshuman Singh 