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 as cp
N = 8
ans = []

def out(M):
    for i in range(N):
        for j in range(N):
            print(M[i][j], end="")
        print("")
    
def DFS(r,c,dp,dn,qn):
    global ans
    if qn == N:
        for h in range(N):
            for w in range(N):
                if r[h] & c[w] & dp[h+w] & dn[w-h+7]:
                    ans.append([h,w])
                    return True
        return False

    for h in range(N):
        for w in range(N):
            if r[h] & c[w] & dp[h+w] & dn[w-h+7]:
                new_r = cp.deepcopy(r)
                new_c = cp.deepcopy(c)
                new_dp = cp.deepcopy(dp)
                new_dn = cp.deepcopy(dn)
                new_r[h],new_c[w],new_dp[h+w],new_dn[w-h+7] = False,False,False,False
                if DFS(new_r,new_c,new_dp,new_dn,qn+1):
                    ans.append([h,w])
                    return True
    return False


def main():
    row = [True]*N
    col = [True]*N
    dp = [True]*(2*N-1)
    dn = [True]*(2*N-1)
    k = int(input())
    MAP = [["." for _ in range(N)] for __ in range(N)]
    for _ in range(k):
        h,w = map(int,input().split())
        MAP[h][w] = "Q"
        row[h] = False
        col[w] = False
        dp[w+h] = False
        dn[w-h+7] = False
    
    DFS(row,col,dp,dn,k+1)

    
    for h,w in ans:
        MAP[h][w] = "Q"

    out(MAP)

main()

