#initial matrix
#end matrix
#Hamming value calculation
#Mannathen value calculation.
#distance of the indexes of the current matrix to where they should be in the ending matrix.
#Subtraction must be done with absolute value.
#Because: If the element that should be at position [2][2] is at position [0][0], the distance gives a negative result.
#Heuristic value is the sum of mannathen and hamming values.
#heuristic value intuitively represents our distance from the outcome.
#Returns the row and column containing element 0 in the matrix
#Adds to the list the places where the number 0 can move within the matrix
#clears the list before each step
#The function requires a matrix, row and column as values.
#If newly created matrices already exist, we do not add them to the list.
#This way we don't go through the same step again.
#and the function does not stay in an infinite loop
#We print the matrix.
#We give 2 seconds of sleep time. Because the matrixs flow so fast.
#Sıfır sayısının gidebileceği yere sıfır sayısını alıyoruz.
#Adds the new matrices we created to the list.
#This function creates matrices which will be one of our next steps.
#A-Star Algorithm
#Clear main list and add starting matrix to the end of the list
#Finally send the last element of the main list to the function
