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:
k = int(raw_input())

maxlayer = 0
res = [0]*100
idex = 1

i5 = 13
while (5 ** i5 > k): i5 -= 1
if (i5 > 0):
    k -= 5 ** i5
    maxlayer = max(maxlayer, i5)

while k > 0:    
    k_max = 0
    k_lay = 0    
    for i in range(0,33):        
        if k < 1<<i: break        
        k_max = k/(2**i)*(2**i)
        k_lay = i    
    res[k_lay] = k/(2**k_lay)
    k -= k_max    
    maxlayer = max(k_lay, maxlayer)
    
n = 2 + (maxlayer - i5 + i5 * 5)
a = []

for i in range(0,maxlayer + 1):
    if res[i] > 0: n += (maxlayer - i + i * 2) * res[i]

print n
for i in range(n): a.append(['N'] * n)

while res[0] > 0:
    start = 0
    for i in range(maxlayer):
        idex += 1
        a[start][idex], a[idex][start] = 'Y', 'Y'
        start = idex
    if maxlayer == 0:
        a[0][1], a[1][0] = 'Y', 'Y'
    else: a[1][idex], a[idex][1] = 'Y', 'Y'
    res[0] -= 1

if i5 > 0:
    start = 0
    if (i5 < maxlayer):        
        for j in range(maxlayer-i5):
            idex += 1
            a[start][idex], a[idex][start] = 'Y', 'Y'
            start = idex            
    idex += 1
    for j in range(5):
        a[start][idex+j], a[idex+j][start] = 'Y', 'Y'    
    for j in range(i5-1):            
        for x in range(5):
           for y in range(5):                    
                a[idex + x][idex+5+y], a[idex+5+y][idex + x] = 'Y','Y'
        idex = idex + 5
    for j in range(5):
        a[1][idex+j], a[idex+j][1] = 'Y', 'Y'    
    idex = idex + 4


for i in range(1, maxlayer + 1):
    while res[i] > 0:
        res[i] -= 1
        start = 0
        if (i < maxlayer):
            for j in range(maxlayer-i):
                idex += 1
                a[start][idex], a[idex][start] = 'Y', 'Y'
                start = idex
        a[start][idex+1], a[idex+1][start] = 'Y', 'Y'
        a[start][idex+2], a[idex+2][start] = 'Y', 'Y'
        
        idex += 1
        for j in range(i-1):            
            for x in range(2):
                for y in range(2):                    
                    a[idex + x][idex+2+y], a[idex+2+y][idex + x] = 'Y','Y'
            idex = idex + 2
        a[idex][1], a[1][idex] = 'Y', 'Y'
        a[idex + 1][1], a[1][idex + 1] = 'Y','Y'
        idex = idex + 1
   
for i in range(n): print ''.join(a[i])