6 30 s 128 MB

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.

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.

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 |