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...
#include<stdio.h>
#include<string.h>
int s[8][8],a[8],book[8],b[16],c[16];
void cn(int x)
{
    int i,j;
    if(x==8)
    {
        for(i=0; i<8; i++)
        {
            for(j=0; j<8; j++)
            {
                if(s[i][j])
                {
                    if(a[i]!=j)
                        return;
                }
            }
        }
        for(i=0; i<8; i++)
        {
            for(j=0; j<8; j++)
            {
                if(a[i]==j)
                    printf("Q");
                else
                    printf(".");
            }
            printf("\n");
        }
        return;
    }
    for(i=0; i<8; i++)
    {
        if(book[i]||b[x+i]||c[x-i+7])
            continue;
        a[x]=i;
        book[i]=b[x+i]=c[x-i+7]=1;
        cn(x+1);
        book[i]=b[x+i]=c[x-i+7]=0;
    }
}
int main()
{
    int r,l,n,i;
    memset(s,0,sizeof(s));
    memset(a,0,sizeof(a));
    memset(book,0,sizeof(book));
    memset(b,0,sizeof(b));
    memset(c,0,sizeof(c));
    scanf("%d",&n);
    for(i=0; i<n; i++)
    {
        scanf("%d%d",&r,&l);
        s[r][l]=1;
    }
    cn(0);
    return 0;
}

