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 solve(n):
  count = 0
  arr = []
  for i in range(1,n+1):
    k = ['.']*n
    if i %2 != 0:
      for c in range(0,n,2):
        k[c] = 'C'
        count += 1
    else:
      for c in range(1,n,2):
        k[c] = 'C'
        count += 1

    arr.append(''.join(k))
  print(count)
  for i in arr:
    print(i, end='\n')
    
def main():
  #arr1 =list(map(int,input().split(' ')))
  #arr1 =input().split(' ')
  #arr2 = []
  n = int(input())
  #for j in range(n):
    #i = input()
    # i = input().split(' ')
    #i = int(''.join(input().split(' ')))
    #arr2 = arr2 + i
  #n = input()
  #t = input()
  solve(n)

main()