Python: X marks the trail

I am trying to make a code that allows the user to track where they have been on a grid (grok introduction to python (2) X marks the trail) I have been working on the code for a while and I think that I'm pretty close but not sure how to correctly format it

the code should work like this:

Grid size: 3
x..
...
...
Direction: right
xx.
...
...
Direction: down
xx.
.x.
...
Direction: right
xx.
.xx
...
Direction: 

but mine displays:

Grid size: 3
[['x', '.', '.'], ['.', '.', '.'], ['.', '.', '.']]
Direction: down
[['x', '.', '.'], ['x', '.', '.'], ['.', '.', '.']]
Direction: right
[['x', '.', '.'], ['x', 'x', '.'], ['.', '.', '.']]
Direction: right
[['x', '.', '.'], ['x', 'x', 'x'], ['.', '.', '.']]
Direction: down
[['x', '.', '.'], ['x', 'x', 'x'], ['.', '.', 'x']]
Direction: left
[['x', '.', '.'], ['x', 'x', 'x'], ['.', 'x', 'x']]

my code is:

g = input('Grid size: ')
gn = int(g)
grid = []
for i in range(gn):
  row = []
  for j in range(gn):
    row.append('.')
  grid.append(row)
grid[0][0]='x'
print(grid)
h = 0
v = 0
m = input("Direction: ")
while m != "":
  if m.lower() == "right":
    h = h+1
    grid[v][h] = 'x'
    print(grid)
    m = input("Direction: ")
  elif m.lower() == "left":
    h = h-1
    grid[v][h]= 'x'
    print(grid)
    m = input("Direction: ")
  elif m.lower() == "up":
    v = v-1
    grid[v][h]= 'x'
    print(grid)
    m = input("Direction: ")
  elif m.lower() == "down":
    v = v+1
    grid[v][h]= 'x'
    print(grid)
    m = input("Direction: ")

Someone, PLEASE help I can't figure out how to join the lists together (each on a new line)

You could create function to print the grid

def show_grid(grid):
    for line in grid:
        print(''.join(line))