A developer is working on an application that requires $n$ inputs to run, where the value of the $i^{th}$ input in the input file is represented by the array val$[$i$].$ Before passing the input file to the application, the developer needs to encrypt it so that it is perfectly encrypted.

The developer can encrypt the file by performing the following operation any number of times:

select arny integer value in the file and replace it with any substring of its digits.

Note: A substring of an integer is any contiguous segment of digits of the integer. For example, $728,86,2,$ and $37$ are substrings of the integer $372862,$ but $322$ and $7862$ are not.

The input file is perfectly encrypted if the array of inputs is sorted. The developer wants to find the lexicographically