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:
g = [ [False for i in range(100)] for i in range(100) ]
k = int(raw_input())
g[1][6] = True
for i in range(1, 31):
	a = 3 + 1 + ( i - 1 ) * 3
	b, c, x, y ,z = (a + 1 , a + 2 , a + 3 , a + 4, a + 5)
	g[a][x] = g[b][x] = g[a][y] = g[b][y] = g[c][z] = True
g[94][2] = g[95][2] = True
i = 30; j = 6
while i >= 0:
	if k & 1 << i :
		g[j][j - 1] = True
	i -= 1; j += 3
print 96
for i in range(1 , 97):
	out = []
	for j in range(1 , 97):
		out += ["Y" if g[i][j] or g[j][i] else "N"]
	print ''.join(out)