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:
M = [[0 for i in range(0, 200)] for i in range(0, 200)]
def add(a, b):
	M[a][b] = M[b][a] = 1

A = [0 for i in range(0, 200)]
add(1, 3)
A[99] = 1
for i in range(3, 101):
	x = (i + 1) if i != 100 else 2
	add(i, x)
	A[100-i+1] = i
A[0] = 2

def deal():
	global k
	i = 0
	while (1<<i) <= k:  i += 1
	i -= 1
	k -= (1<<i) # subtract
	return i

n = 100
k = input() # input here
L = deal()
B = [0 for i in range(0, 200)]
B[0] = 1
for i in range(1, L):
	n += 1
	B[i] = n
B[L] = 2
for i in range(1, L+1):
	add(B[i-1], n+1)
	add(B[i-1], n+2)
	add(n+1, B[i])
	add(n+2, B[i])
	n += 2

while k > 0:
	L1 = deal()
	L2 = (L - L1) * 2 - 1
	add(B[L1], A[L2])

print n
for i in range(1, n+1):
	s = ""
	for j in range(1, n+1):
		s += "Y" if M[i][j] == 1 else "N"
	print s