The goal of 8 Queens Problem is to put eight queens on a chess-board such that none of them threatens any of others. A queen threatens the squares in the same row, in the same column, or on the same diagonals as shown in the following figure.

<image>


For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.

Constraints

* There is exactly one solution

Input

In the first line, an integer $k$ is given. In the following $k$ lines, each square where a queen is already placed is given by two integers $r$ and $c$. $r$ and $c$ respectively denotes the row number and the column number. The row/column numbers start with 0.

Output

Print a $8 \times 8$ chess board by strings where a square with a queen is represented by 'Q' and an empty square is represented by '.'.

Example

Input

2
2 2
5 3


Output

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...
N = 8
flag_row = [False]*N
flag_col = [False]*N
flag_diag_right = [False]*(2*N-1)
flag_diag_left  = [False]*(2*N-1)
B = [ [False for n in range(N)] for n in range(N)]

def ShowBoard():
    for i in range(N):
        for j in range(N):
            if B[i][j] :
                if flag_row[i] != j:
                    return

    for i in range(N):
        for j in range(N):
            if flag_row[i] == j:
                print("Q", end = "")
            else:
                print(".", end = "")
        print()

def SetQueen(i):
    if i == N  :
        ShowBoard()
        return

    for j in range(N):
        if flag_col[j] == False and flag_diag_left[i + j] == False and flag_diag_right[i - j + (N -1)] == False :

            flag_row[i] = j
            flag_col[j] = True
            flag_diag_left[i + j] = True
            flag_diag_right[i - j + (N -1)] = True

            SetQueen(i + 1)

            flag_row[i] = False
            flag_col[j] = False
            flag_diag_left[i + j] = False
            flag_diag_right[i - j + (N -1)] = False

def Main():
    K = int(input())

    for k in range(K):
        r, c = map(int, input().split())
        B[r][c] = True

    SetQueen(0)

Main()
