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:
__author__ = 'Shailesh'

import math
k = int(raw_input())

forms = [['YN', 'N', 'Y', 'N', 'N', 'N'],
        ['NN', 'Y', 'N', 'Y', 'N', 'N'],
        ['NN', 'N', 'Y', 'N', 'Y', 'N'],
        ['NN', 'N', 'N', 'Y', 'N', 'Y'],
        ['NY', 'N', 'N', 'N', 'Y', 'N']]
vertice1 = ['Y', 'N', 'N', 'N', 'N']
vertice2 = ['N', 'N', 'N', 'N', 'Y']
def addvertices(data, length, size):
    inserted = len(data[0])
    lengths = [length] * size + [1] * (5 - size)
    for i in xrange(len(lengths)):
        data[0] += vertice1[i] * lengths[i]
        data[1] += vertice2[i] * lengths[i]
    for i in xrange(2, inserted):
        data[i] += "N" * sum(lengths)
    index = inserted
    for f in xrange(len(forms)):
        form = forms[f]
        line = form[0] + "N" * (inserted - 2)
        for i in xrange(1, len(form)):
            line += form[i] * lengths[i - 1]
        for i in xrange(lengths[f]):
            data[index] = line
            index += 1

def getrootfloor(num, root):
    rf = int(math.pow(num, 1.0 / root))
    rem = num - math.pow(rf, root)
    return rf, rem

def getroots(num, root):
    roots = []
    limit = math.pow(2, root)
    while num >= limit:
        rf, num = getrootfloor(num, root)
        roots.append(rf)
    return roots, int(num)

roots, rem = getroots(k, 5)
n = sum(roots) * 5 + 2
temp = rem
if rem >= 16:
    rem -= 16
    n += 9
if rem >= 8:
    rem -= 8
    n += 8
if rem >= 4:
    rem -= 4
    n += 7
if rem > 0:
    n += rem * 5
rem = temp
data = ["" for i in xrange(n)]
data[0] = "NN"
data[1] = "NN"

for root in roots:
    addvertices(data, root, 5)
if rem >=16:
    rem -= 16
    addvertices(data, 2, 4)
if rem >=8:
    rem -= 8
    addvertices(data, 2, 3)
if rem >= 4:
    rem -= 4
    addvertices(data, 2, 2)
for i in xrange(rem):
    addvertices(data, 1, 5)

print n
for line in data:
    print line