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
def print_chessboard(size: int) -> None:
    n_coders = size * size // 2
    line = ['C.' * (size // 2), '.C' * (size // 2)]

    if size % 2 != 0:
        n_coders += 1
        line[0] += 'C'
        line[1] += '.'

    print(n_coders)

    for i in range(size):
        print(line[i % 2])

    return


def main() -> int:
    n = int(input())
    print_chessboard(n)

    return 0


if __name__ == '__main__':
    main()