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 place_diag(board, r, c, n):
    num = 0
    while r < n and c < n:
        board[r][c] = True
        r, c, num = r + 1, c + 1, num + 1
    return num

def print_board(board):
    for row in board:
        print ''.join('C' if c else '.' for c in row)

if __name__ == '__main__':
    n = int(raw_input(''))
    board = [[False for _ in xrange(n)] for _ in xrange(n)]
    changed = 0
    for r in xrange(0, n, 2):
        changed += place_diag(board, r, 0, n)

    if n >= 2:
        for c in xrange(2, n, 2):
            changed += place_diag(board, 0, c, n)
    print changed
    print_board(board)
