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 run(n):
    rtn, total = [['.'] * n for i in xrange(n)], 0
    for i in xrange(n):
        for j in xrange(n):
            if i % 2 == 0 and j % 2 == 0:
                rtn[i][j] = 'C'
                total += 1
            elif i % 2 == 1 and j % 2 == 1:
                rtn[i][j] = 'C'
                total += 1

    return [total, rtn]

if __name__ == "__main__":
    inpt = raw_input()
    args = [int(el) for el in inpt.split(' ')]
    rtn = run(*args)
    if type(rtn) is list:
        for el in rtn:
            if type(el) is list:
                for e in el:
                    print "".join(e)

            else:
                print el

    else:
        print rtn
