You are given two integers l and r, and a string directions.

For any integer x, consider its $16$ digit representation padded with leading zeros if it contains fewer than $16$ digits. These $16$ digits are placed into a $4 \times 4$ grid in row major order, filling rows from top to bottom and columns from left to right, with the top left cell at $(0, 0)$ and the bottom right cell at $(3, 3)$.

A path on the grid begins at cell $(0, 0)$ and ends at cell $(3, 3)$. The path follows the sequence of moves given by directions, where 'D' denotes moving down one cell and 'R' denotes moving right one cell.

An integer x is defined as good if the sequence of digits visited along the path is non decreasing.

Return the count of good integers x such that l $\le x \le$ r.

Constraints:

• $1 \le$ l $\le$ r $\le 9 \times 10^{15}$

• directions.length $= 6$

• directions consists of exactly three 'D' characters and three 'R' characters.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.