Python: Gridmap can't calculate print out the route in the Grid Map

Question

I am trying to implement GridMap in python and trying implement str(self) that prints, The Starting Location, Ending Location and the Route between them. I've managed to do the starting and ending locations but not the Route between them. when i try to calculate the route it doesn't appear on my gridmap

class GridMap:
    def __init__(self, row, column):
        self.row = row
        self.column = column
        self.start_col = None
        self.start_row = None
        self.end_col = None
        self.end_row = None
        self.change_column = None
        self.change_row = None

    def add_start(self, row, column):
        self.start_row = row
        self.start_col = column

    def add_end(self, row, column):
        self.end_col = column
        self.end_row = row
        self.DX = self.start_row - self.end_row
        self.DY = self.start_col - self.end_col

    def __str__(self):
        new_str = ""
        #new_str += ("0" * self.row + "\n") * self.column
        for i in range(self.column):
            new_str += "\n"
            for j in range(self.row):
                if j == self.start_col and i == self.start_row:
                    new_str += "A"
                elif j == self.end_col and i == self.end_row:
                    new_str += "Z"
                elif i == self.change_row and j == self.end_col:
                        new_str += "X"
                        if self.change_row != 0:
                            if self.change_row > 0:
                                self.change_row - 1
                            else:
                                self.DX + 1
                elif i == self.end_row  and j ==self.DY :
                        new_str += "X"
                        
                else:
                    new_str += "0"
        return new_str
        
m = GridMap(5, 5)
print(m)
m.add_start(4, 4)
print(m)
m.add_end(0, 3)
print(m)

expected result
00000
00000
00000
00000
00000

00000
00000
00000
00000
0000A

000Z0
000X0
000X0
000X0
000XA

got:

00000
00000
00000
00000
00000

00000
00000
00000
00000
0000A

0X0Z0
00000
00000
00000
0000A