Matchsticks are ideal tools to represent numbers. A common way to represent the ten decimal digits with matchsticks is the following:
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 |
---|---|
4 3 6 7 15 |
7 7 6 111 8 711 108 7111111 |