Problem: Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with n vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2."

Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to k?

Input

The first line contains a single integer k (1 ≤ k ≤ 109).

Output

You should output a graph G with n vertexes (2 ≤ n ≤ 1000). There must be exactly k shortest paths between vertex 1 and vertex 2 of the graph.

The first line must contain an integer n. Then adjacency matrix G with n rows and n columns must follow. Each element of the matrix must be 'N' or 'Y'. If Gij is 'Y', then graph G has a edge connecting vertex i and vertex j. Consider the graph vertexes are numbered from 1 to n.

The graph must be undirected and simple: Gii = 'N' and Gij = Gji must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them. 

Examples

Input

2

Output

4
NNYY
NNYY
YYNN
YYNN

Input

9

Output

8
NNYYYNNN
NNNNNYYY
YNNNNYYY
YNNNNYYY
YNNNNYYY
NYYYYNNN
NYYYYNNN
NYYYYNNN

Input

1

Output

2
NY
YN

Note

In first example, there are 2 shortest paths: 1-3-2 and 1-4-2.

In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.

Solution (in PYTHON):

Solution:
k = int(raw_input())
hex_str = list(reversed(hex(k)[2:]))
total_nodes = 2

for i, c in enumerate(hex_str):
  if c != '0':
    total_nodes += 16 * i + int(c, 16) + 7 - i

# set up matrix
#mat = [["N"] * total_nodes] * total_nodes
mat = [["N" for i in xrange(total_nodes)] for j in xrange(total_nodes)]
print total_nodes

offset = 2
for i, c in enumerate(hex_str):
  if c == '0': continue
  arr = ([16] * i) + [int(c, 16)] + [1] * (7 - i)
  #print arr
  #print offset

  for j in xrange(arr[0]):
    mat[0][offset + j] = "Y"
    mat[offset + j][0] = "Y"
  offset += arr[0]
  #print offset

  for j in xrange(len(arr) - 1):
    for a in xrange(arr[j]):
      for b in xrange(arr[j+1]):
        mat[offset - a - 1][offset + b] = "Y"
        mat[offset + b][offset - a - 1] = "Y"
    offset += arr[j+1]
    #print offset

  for j in xrange(arr[7]):
    mat[1][offset-j-1] = "Y"
    mat[offset-j-1][1] = "Y"
  #print offset

for row in mat:
  print ''.join(row)