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:
lst = [(i, 2 ** i) for i in xrange(32)]

K = int(raw_input())

candi = []
for i, val in lst:
    if K & val == 0:
        continue
    candi.append(i)

leng = candi[-1]

edge = []

def addedge(a, b):
    edge.append((a, b))

lst = range(2, 40)
for i in lst[:-1]:
    addedge(i, i+1)
addedge(1, lst[-1])

N = lst[-1] + 1

for i in candi:
    if i == 0:
        addedge(0, lst[0])
    else:
        addedge(0, N)
        addedge(0, N+1)
        N += 2

        for j in xrange(i-1):
            addedge(N-1, N)
            addedge(N-2, N+1)
            addedge(N-2, N)
            addedge(N-1, N+1)
            N += 2

        addedge(N - 1, lst[i])
        addedge(N - 2, lst[i])

ans = [['N' for j in xrange(N)] for i in xrange(N)]
for a, b in edge:
    ans[a][b] = 'Y'
    ans[b][a] = 'Y'

#print edge
print N
for row in ans:
    print ''.join(row)