#1616 TwoRegisters

30 s   128 MB  

Description

You have a very simple computer whose memory consists only of two registers X and Y. Each of them can store a positive integer. The computer is so simple that it only has two different instructions (between brackets is the name of each instruction):

[X] X := X + Y
[Y] Y := X + Y

As you may have imagined, both instructions compute the sum of both registers and store the result in one of them, overwriting its previous content. A program for this computer is simply a sequential list of zero or more instructions. When a program starts in this computer, both registers are initialized to 1. For instance, if the program is "XXYYX" then the following happens:

  X | Y | ins | execute
----+---+-----+------------
  1 | 1 | [X] | X := X + Y
----+---+-----+------------
  2 | 1 | [X] | X := X + Y
----+---+-----+------------
  3 | 1 | [Y] | Y := X + Y
----+---+-----+------------
  3 | 4 | [Y] | Y := X + Y
----+---+-----+------------
  3 | 7 | [X] | X := X + Y
----+---+-----+------------
 10 | 7 |

You will be given an int r. Return the shortest program for the described computer that makes register X end with value r. Register Y may contain any value. If there are several such programs, return the one that comes earliest lexicographically.

Input

The first line of the input gives the number of test cases, T (1 <= T <= 200).

For each test case one positive integer r, which is between 2 and 1000000, inclusive, will be given.

Output

For each test case, print the shortest program as explained in the problem statement, in one line.

Sample Input

Sample Output

4
10
3
20
34
XXYYX
XX
XYYYYXX
XYXYXYX