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
import math


def coder(n):
    cant = math.ceil(n ** 2 / 2)
    m = list()
    for i in range(n):
        if n % 2 == 0 and i % 2 == 0:
            m.append("C." * (n // 2))
        elif n % 2 == 0 and i % 2 != 0:
            m.append(".C" * (n // 2))
        elif n % 2 != 0 and i % 2 == 0:
            m.append("C." * (n // 2) + "C")
        elif n % 2 != 0 and i % 2 != 0:
            m.append(".C" * (n // 2) + ".")
    return [cant, m]


n = int(input().strip())
r = coder(n)
print(r[0])
for i in range(n):
    print(r[1][i])
