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...
import copy

n = int(input())

dotsa = []
for _ in range(n):
    y,x = map(int,input().split(" "))
    dotsa.append([y,x])

pattern = []
pattern.append(dotsa)


for y in range(8):
    nextpattern = []
    #print("#######")
    #print(pattern)
    for pat in pattern:
        #print(";;;;;;;;;;;;;;;;;;;;;")
        #print(pat)
        flag = False
        for dot in pat:
            if dot[0] == y:
                flag = True
                break

        if flag:
            nextpattern = pattern
            continue

        ifFound = False
        for x in range(8):
            ank = len(pat)
            flag2 = True
            for i in range(ank):
                if abs(pat[i][0]-y) == abs(pat[i][1]-x) or pat[i][1] == x:
                    flag2 = False
                    break
            if flag2:
                #print("appended")
                #print(y)
                #print(x)
                tmp = copy.deepcopy(pat)
                tmp.append([y,x])
                nextpattern.append(tmp)
        #print("x loop end")
    pattern = nextpattern

ans = pattern[0]
board = [["."]*8 for i in range(8)]
#print(ans)
for ele in ans:
    board[ele[0]][ele[1]] = "Q"
for row in board:
    print(''.join(map(str,row)))

