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=str(input())
l=len(k)
paths=[]
for i in range(l):
    paths.append([1]*i+[int(k[i])]+[10]*(l-i-1))
lens = [sum(p) for p in paths]
n = sum(lens)+2
m = ['']*n
m[0] = 'N'*2
for i in range(len(paths)):
    m[0] += 'Y'*paths[i][0]+'N'*(lens[i]-paths[i][0])
m[1] = 'N'
for i in range(len(paths)):
    m[1] += 'N'*(lens[i]-paths[i][-1])+'Y'*paths[i][-1]
ind=2
for p in paths:
    for i in range(len(p)-1):
        for j in range(p[i]):
            m[ind] = 'N'*(p[i]-j)+'Y'*(p[i+1])+'N'*n
            ind+=1
    for j in range(p[-1]):
        m[ind] = 'N'*n
        ind+=1
m2=['']*n
for i in range(n):
    m2[i] = ''
    for j in range(i):
        m2[i]+=m2[j][i]
    m2[i]+=m[i][:n-i]
print(len(m2))
for s in m2:
    print(s)