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;
  cin >> n;
  unsigned long long m = (n * n + 1) / 2;
  cout << m << "\n";
  bool b = 1;
  for (int i = 0; i != n; ++i) {
    for (int j = 0; j != n; ++j) {
      cout << (b ? 'C' : '.');
      b = !b;
    }
    if ((n & 1) == 0) b = !b;
    cout << "\n";
  }
  return 0;
}
