Certain positive integers have their decimal representation consisting only of ones and zeros, and having at least one digit one, e.g. 101. If a positive integer has not such a property, one can try to multiply it by some positive integer to find out whether the product has this property.

Task

Write a program that:

• reads from the text file JED.IN positive integers n not greater than 20000,
• for each integer read computes a correct answer,
• writes the answer to the text file JED.OUT.

Input

The file JED.IN contains in the first line a positive integer K<1000. In consecutive lines there is a sequence of K numbers in the range of [1..20000], one number per line. The numbers in the file JED.IN are written correctly, and your program need not verify that.

Output

Each line of the file JED.OUT, starting with the first, should contain:

• either only one word BRAK,
• or exactly one positive integer being a multiple of a successive number given in the input; each multiple must be a number composed only of digits 0 and 1, and has to be written with no spaces between the digits.

Example

6
17
11011
17
999
125
173

11101
11011
11101
111111111111111111111111111
1000
1011001101

Your program should look for the file JED.IN in the current directory and create the file JED.OUT also in the current directory. The source file containing the program written by you should be named JED.???, where ??? are substituted by at most three-letter abbreviation of the programming language used. The same program in an executable form should be written in a file JED.EXE.

^* The task comes from a collection of Romanian problems. Dr. Andrzej Walat has compiled the contents and he is the author of the solutions.