Iahub likes chess very much. He even invented a new chess piece named Coder. A Coder can move (and attack) one square horizontally or vertically. More precisely, if the Coder is located at position (x, y), he can move to (or attack) positions (x + 1, y), (x–1, y), (x, y + 1) and (x, y–1).

Iahub wants to know how many Coders can be placed on an n × n chessboard, so that no Coder attacks any other Coder.

Input

The first line contains an integer n (1 ≤ n ≤ 1000).

Output

On the first line print an integer, the maximum number of Coders that can be placed on the chessboard.

On each of the next n lines print n characters, describing the configuration of the Coders. For an empty cell print an '.', and for a Coder print a 'C'.

If there are multiple correct answers, you can print any.

Examples

Input

2


Output

2
C.
.C
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, s, r, c = 1, x, y;
  cin >> n;
  s = n * n;
  (n % 2 == 0) ? r = s / 2 : r = (s + 1) / 2;
  cout << r << "\n";
  while (c <= s) {
    if (c % n == 0)
      x = n;
    else
      x = c % n;
    y = ((c - 1) / n) + 1;
    r = x + y;
    if (r % 2 == 0)
      cout << "C";
    else
      cout << ".";
    if (c % n == 0)
      cout << "\n";
    else
      cout << "";
    c++;
  }
}
