A recycling problem  



Recycling glass requires that the glass be separated by color into one of three 
categories: brown glass, green glass, and clear glass. In this problem you will be 
given three recycling bins, each containing a specified number of brown, green and 
clear bottles. In order to be recycled, the bottles will need to be moved so that 
each bin contains bottles of only one color. 

The problem is to minimize the number of bottles that are moved. You may assume that 
the only problem is to minimize the number of movements between boxes. 

For the purposes of this problem, each bin has infinite capacity and the only 
constraint is moving the bottles so that each bin contains bottles of a single 
color. The total number of bottles will never exceed 2^31. 


The Input

The first line of the input contains a single integer n, denoting the number of 
instances of the problem you must solve. The next n lines with each line each 
contain 9 integers. The first three integers represent the number of brown, green, 
and clear bottles (respectively) in bin number 1, the second three represent the 
number of brown, green and clear bottles (respectively) in bin number 2, and the 
last three integers represent the number of brown, green, and clear bottles 
(respectively) in bin number 3. 

For example, the line 10 15 20 30 12 8 15 8 31 
indicates that there are 20 clear bottles in bin 1, 12 green bottles in bin 2, and 
15 brown bottles in bin 3. 

Integers on a line will be separated by one or more spaces. Your program should 
process all n instances in the input file. 


The Output

For each instance there will be one line of output indicating what color bottles 
go in what bin to minimize the number of bottle movements. You should also print 
the minimum number of bottle movements. 

The output should consist of a string of the three upper case characters 'G', 'B', 
'C' (representing the colors green, brown, and clear) representing the color 
associated with each bin. 

The first character of the string represents the color associated with the first bin, 
the second character of the string represents the color associated with the second 
bin, and the third character represents the color associated with the third bin. 

The integer indicating the minimum number of bottle movements should follow the string. 

If more than one order of brown, green, and clear bins yields the minimum number of 
movements then the alphabetically first string representing a minimal configuration 
should be printed. 


Sample Input

2
1 2 3 4 5 6 7 8 9
5 10 5 20 10 5 10 20 10

Sample Output

BCG 30
CBG 50