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
# cf 384 A 800
n = int(input())

rows = []
c = 0

for i in range(n):
    c += (n // 2)
    if n % 2 != 0 and i % 2 == 0:
        c += 1
    if i % 2 == 0: # even
        row = [ "C." ] * (n // 2)
        if n % 2 == 1:
            row += [ "C" ]
    else:
        row = [ ".C" ] * (n // 2)
        if n % 2 == 1:
            row += [ "." ]
    rows.append(row)

print(c)
for row in rows:
    print("".join(row))
