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...
def sakuzyo(i):
    if koteirow[i] == 1:
        sakuzyo(i-1)
    else:
        for j in range(N):
            if haiti[i][j] == 'Q':
                #print('delete {} {}'.format(i, j))
                haiti[i][j] = '.'
                row[i] = 0
                col[j] = 0
                dpos[i + j] = 0
                dneg[i - j + (N - 1)] = 0
                if j == N-1:
                    sakuzyo(i-1)
                else:
                    sounyuu(i, j+1)


def sounyuu(i, j):
    if koteirow[i] == 0:
        for k in range(j, N):
            flag = 0
            if col[k] == 0 and dpos[i+k] == 0 and dneg[i-k+(N-1)] == 0:
                haiti[i][k] = 'Q'
                #print('add {} {}'.format(i, k))
                row[i] = 1
                col[k] = 1
                dpos[i+k] = 1
                dneg[i-k+(N-1)] = 1
                flag = 1
                if i == N-1:
                    for o in range(N):
                        for p in range(N):
                            print(haiti[o][p], end='')
                        print()
                    exit()
                else:
                    sounyuu(i+1, 0)
        if flag == 0:
            sakuzyo(i-1)
    elif i == N-1:
        for o in range(N):
            for p in range(N):
                print(haiti[o][p], end='')
            print()
        exit()
    else:
        sounyuu(i+1, j)


k = int(input())
data = [list(map(int, input().split()))for _ in range(k)]

N = 8
row = [0]*N
col = [0]*N
dpos = [0]*(N*2-1)
dneg = [0]*(N*2-1)
haiti = [['.']*N for _ in range(N)]
koteirow = [0]*N

for i in data:
    haiti[i[0]][i[1]] = 'Q'
    row[i[0]] = 1
    col[i[1]] = 1
    dpos[i[0]+i[1]] = 1
    dneg[i[0] - i[1] + (N - 1)] = 1
    koteirow[i[0]] = 1

sounyuu(0, 0)


