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 seta(a, x, y, val):
    if x < 0 or x > n - 1:
        return
    if y < 0 or y > n - 1:
        return
    a[x][y] = val
n = input()
a = [[],[]]
a[1] = (".C" * n)[:n]
a[0] = ("C." * n)[:n]
print (n * n + 1) / 2
for i in xrange(n):
    print a[i % 2]
