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 ≤ 10^9).


-----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 G_{ij} 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: G_{ii} = 'N' and G_{ij} = G_{ji} 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.

Difficulty: competition

Starter code:

Solutions:
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)


n, m = 337, int(input())
p = [['N'] * n for i in range(n)]
def f(i, j): p[i][j] = p[j][i] = 'Y'

k = 6 + 15 * 5
for j in range(2, 6): f(1, j)
for i in range(6, k, 5):
    for j in range(i - 4, i): f(i, j)
    for j in range(i + 1, i + 5): f(i, j)

q, d, s = 4 ** 15, 0, k
while q:
    if m >= q:
        t = m // q
        m -= t * q
        if d == 0:
            for j in range(k - t, k): f(0, j)
        else:
            f(0, s)
            for i in range(s, s + d): f(i, i + 1)
            s += d
            for j in range(k - t, k): f(s, j)
            s += 1
    k -= 5
    d += 2
    q //= 4

print(s)
for i in range(s): print(''.join(p[i][: s]))

n, m, cnt = int(input()), 148, 0
ans = [['N'] * m for i in range(m)]

def edge(i, j):
    ans[i][j] = ans[j][i] = 'Y'

def node(*adj):
    nonlocal cnt
    i = cnt
    cnt += 1
    for j in adj:
        edge(i, j)
    return i

start, end, choice = node(), node(), node()
if n&1:
    edge(choice, end)
for i in range(1, 30):
    end, choice = node(node(end), node(end)), node(node(choice))
    if n&(1<<i):
        edge(choice, end)
edge(start, choice)

print(m)
for line in ans:
    print(''.join(line))




# Made By Mostafa_Khaled


k = int(input())


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

def add_edge(a, b):
    nonlocal 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])))


N = int(input())
b = bin(N)[2:][::-1]
count = len(b)-1

def print_matrix(m):
    print(len(m))
    for i in range(len(m)):
        print("".join(m[i]))

m = [['N' for i in range(2*(len(b))+count)] for j in range(2*(len(b))+count)]
for i in range(count-1):
    val = len(m)-count+i
    m[val][val+1] = 'Y'
    m[val+1][val] = 'Y'

if count>0:
    m[len(m)-1][1] = 'Y'
    m[1][len(m)-1] = 'Y'

#print_matrix(m)
c = 0
c2 = len(m)-count
for i in range(0, len(m)-count, 2):
    if i >= len(m)-2-count and i != 0:
        m[i][1] = 'Y'
        m[i+1][1] = 'Y'
        m[1][i+1] = 'Y'
        m[1][i] = 'Y'
    elif i < len(m)-2-count:
        m[i][i+2] = 'Y'
        m[i][i+3] = 'Y'
        m[i+2][i] = 'Y'
        m[i+3][i] = 'Y'
        if i != 0:
       	    m[i+1][i+2] = 'Y'
       	    m[i+1][i+3] = 'Y'
       	    m[i+2][i+1] = 'Y'
       	    m[i+3][i+1] = 'Y'
    if b[c] =='1':
        if i == len(m)-count-2:
            c2 = 1
        #print_matrix(m)
        m[i][c2] = 'Y'
        m[c2][i] = 'Y'
        if i != 0:
            m[i+1][c2] = 'Y'
            m[c2][i+1] = 'Y'
    c2+=1
        #print_matrix(m)
    c+=1

print(len(m))
for i in range(len(m)):
    print("".join(m[i]))



N = int(input())
b = bin(N)[2:][::-1]
count = len(b)-1

def print_matrix(m):
    print(len(m))
    for i in range(len(m)):
        print("".join(m[i]))

m = [['N' for i in range(2*(len(b))+count)] for j in range(2*(len(b))+count)]
for i in range(count-1):
    val = len(m)-count+i
    m[val][val+1] = 'Y'
    m[val+1][val] = 'Y'

if count>0:
    m[len(m)-1][1] = 'Y'
    m[1][len(m)-1] = 'Y'

#print_matrix(m)
c = 0
c2 = len(m)-count
for i in range(0, len(m)-count, 2):
    if i >= len(m)-2-count and i != 0:
        m[i][1] = 'Y'
        m[i+1][1] = 'Y'
        m[1][i+1] = 'Y'
        m[1][i] = 'Y'
    elif i < len(m)-2-count:
        m[i][i+2] = 'Y'
        m[i][i+3] = 'Y'
        m[i+2][i] = 'Y'
        m[i+3][i] = 'Y'
        if i != 0:
       	    m[i+1][i+2] = 'Y'
       	    m[i+1][i+3] = 'Y'
       	    m[i+2][i+1] = 'Y'
       	    m[i+3][i+1] = 'Y'
    if b[c] =='1':
        if i == len(m)-count-2:
            c2 = 1
        #print_matrix(m)
        m[i][c2] = 'Y'
        m[c2][i] = 'Y'
        if i != 0:
            m[i+1][c2] = 'Y'
            m[c2][i+1] = 'Y'
    c2+=1
        #print_matrix(m)
    c+=1

print(len(m))
for i in range(len(m)):
    print("".join(m[i]))