Problem K

Matchsticks are ideal tools to represent numbers. A common way to represent the ten decimal digits with matchsticks is the following:

\includegraphics[width=\textwidth ]{numbers.png}

This is identical to how numbers are displayed on an ordinary alarm clock. With a given number of matchsticks you can generate a wide range of numbers. We are wondering what the smallest and largest numbers are that can be created by using all your matchsticks.


On the first line one positive number: the number of testcases, at most 100. After that per testcase:

  • One line with an integer $n$ ($2\le n\le 100$): the number of matchsticks you have.


Per testcase:

  • One line with the smallest and largest numbers you can create, separated by a single space. Both numbers should be positive and contain no leading zeroes.

Sample Input 1 Sample Output 1
7 7
6 111
8 711
108 7111111
CPU Time limit 1 second
Memory limit 1024 MB
Statistics Show
Source Northwestern Europe Contest (NWERC) 2008
License Creative Commons License (cc by-sa)

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