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 PYTHON3):

Solution:
k = int(input())


edges = [['N' for i in range(1010)] for j in range(1010)]
vertices = 2

def add_edge(a, b):
    global edges
    edges[a][b] = edges[b][a] = 'Y'


for i in range(1, 29 + 1):
    vertices += 3
    add_edge(i * 3, i * 3 - 1)
    add_edge(i * 3, i * 3 + 2)
    add_edge(i * 3 + 1, i * 3 - 1)
    add_edge(i * 3 + 1, i * 3 + 2)


for bit in range(30):
    if (1 << bit) & k:
        lst = 1
        for i in range((29 - bit) * 2):
            vertices += 1
            add_edge(lst, vertices)
            lst = vertices
        add_edge(lst, 3 * bit + 2)

print(vertices)

if 0:
    for i in range(1, vertices + 1):
        print(i, ':', '\n\t', end='')
        for j in range(1, vertices + 1):
            if edges[i][j] == 'Y':
                print(j, end=' ')
        print('')
else:
    print('\n'.join(map(lambda x: ''.join(x[1:vertices+1]), edges[1:vertices + 1])))