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...
from itertools import permutations as per
from copy import deepcopy
k = int(input())
b = [["."]*8 for _ in range(8)]
st = [[False]*8 for _ in range(8)]

def setQueen(r,c):
    if st[r][c]: return False
    for i in range(8):
        st[i][c] = True
        st[r][i] = True
    d = abs(r-c)
    y,x = d,0
    if r < c: y,x = x,y
    for i in range(8-d): st[y+i][x+i] = True
    d = abs(7-r-c)
    y,x = d,0
    if 7-r < c: y,x = x,y
    for i in range(8-d): st[7-y-i][x+i] = True
    b[r][c] = "Q"
    return True

sr = [True]*8
sc = [True]*8
for _ in range(k):
    r,c = map(int,input().split())
    b[r][c] = "Q"
    setQueen(r,c)
    sr[r] = False
    sc[c] = False

row = [i for i in range(8) if sr[i]]
col = [i for i in range(8) if sc[i]] 

tmpb = b
tmpst = st
for p in per(row):
    b = deepcopy(tmpb)
    st = deepcopy(tmpst)
    for r,c in zip(p,col):
        if not setQueen(r,c): break
    else:
        for i in range(8): print("".join(b[i]))
        break
