Problem: Pavel loves grid mazes. A grid maze is an n × m rectangle maze where each cell is either empty, or is a wall. You can go from one cell to another only if both cells are empty and have a common side.

Pavel drew a grid maze with all empty cells forming a connected area. That is, you can go from any empty cell to any other one. Pavel doesn't like it when his maze has too little walls. He wants to turn exactly k empty cells into walls so that all the remaining cells still formed a connected area. Help him.

Input

The first line contains three integers n, m, k (1 ≤ n, m ≤ 500, 0 ≤ k < s), where n and m are the maze's height and width, correspondingly, k is the number of walls Pavel wants to add and letter s represents the number of empty cells in the original maze.

Each of the next n lines contains m characters. They describe the original maze. If a character on a line equals ".", then the corresponding cell is empty and if the character equals "#", then the cell is a wall.

Output

Print n lines containing m characters each: the new maze that fits Pavel's requirements. Mark the empty cells that you transformed into walls as "X", the other cells must be left without changes (that is, "." and "#").

It is guaranteed that a solution exists. If there are multiple solutions you can output any of them.

Examples

Input

3 4 2
#..#
..#.
#...


Output

#.X#
X.#.
#...


Input

5 4 5
#...
#.#.
.#..
...#
.#.#


Output

#XXX
#X#.
X#..
...#
.#.#

Solution (in PYTHON):

Solution:
n,m,k = map(int, raw_input().split())

dots = []

grid = []

visited = [False]*n*m

for i in range(n):
    row = raw_input()
    grid.append(list(row))
    for j in range(m):
        if row[j] == '.':
            dots.append((i,j))

stack = []

order = []

def dfs(si,sj):
    global stack
    global visited
    global order
    stack = []
    stack.append((si,sj))
    total = 0
    def can_look_at(x,y):
        if not(0 <= x < n and 0 <= y < m):
            return False
        if visited[x*m+y]:
            return False
        if grid[x][y] != '.':
            return False
        return True
    while(stack != []):
        i, j = stack.pop()
        if(not can_look_at(i,j)):
            continue
        visited[i*m+j] = True
        order.append((i,j))
        total += 1
        motions = [(i+di, j+dj) for di,dj in [ (1, 0), (-1, 0), (0, 1), (0, -1)]]
        for i2,j2 in motions:
            if(can_look_at(i2,j2)):
                stack.append((i2, j2))
    return total

blocked_so_far = 0

"""
while(blocked_so_far < k):
    for i,j in dots:
        if(grid[i][j] != '.'):
            continue
        visited = [False]*n*m
        grid[i][j] = 'X'
        start = None
        for si in range(n):
            if start != None:
                break
            for sj in range(m):
                if grid[si][sj] == '.':
                    start = (si, sj)
                    break
        total = dfs(*start)
        if (len(dots) - blocked_so_far - 1 == total):
            blocked_so_far += 1
        else:
            grid[i][j] = '.'
        if blocked_so_far == k:
            break
"""

start = None
for si in range(n):
    if start != None:
        break
    for sj in range(m):
        if grid[si][sj] == '.':
            start = (si, sj)
            break
dfs(*start)

for _i in range(k):
    i,j = order.pop()
    grid[i][j] = 'X'

print '\n'.join(map(''.join, grid))