n this project, you are required to simulate the movements of a beetle in an $8$x$8$ grid. The beetle can move in eight directions: left, right, up$,$ down, up$-$right, up$-$left, down$-$right, and down$-$left. The beetle's initial position $($i$,$j$)$ will be provided by the user. The beetle will then move randomly in one of the eight directions. The program will end when all elements of the grid have been visited at least once.

You can use a $2$x$8$ matrix to determine the direction of the beetle's movement. The matrix is as follows:

Eight directions:

moves Left right up down upright upleft downright downleft

i i i i$-1$ i$+1$ i$-1$ i$-1$ i$+1$ i$+1$

j j$-1$ j$+1$ j j j$+1$ j$-1$ j$+1$ j$-1$

Each time the beetle visits a grid element $($i$,$j$),$ increment a counter for that element. At the end of the program, we want to see the number of visits for each grid element. If the beetle reaches the borders of the grid, it cannot move beyond them. For example, if the beetle is at position $(0,0),$ it can only move down, right, or down$-$right.

When all elements have been visited at least once, print the $8$x$8$ grid and the following probabilities:

The probability of moving left $=$ number of left moves $/$ total number of moves

The probability of moving right $=$ number of right moves $/$ total number of moves

The probability of moving up $=$ number of upward moves $/$ total number of moves

The probability of moving down $=$ number of downward moves $/$ total number of moves

Probability of passing the border $=$ number of unsuccessful attempts to exceed the border $/$ total number of moves