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*?
The first line contains a single integer *k* (1 ≤ *k* ≤ 10<sup class="upper-index">9</sup>).
class Node(object):
    cnt = 0
    def __init__(_, adj=None):
        _.id = Node.cnt
        Node.cnt += 1
        _.adj = adj if adj else []
        _.seen = False

n = int(input())
start = Node()
end = Node()
choose = Node()
for i in range(30):
    if n & (1<<i):
        choose.adj.append(end)
    if i == 29:
        break
    end = Node([Node([end]), Node([end])])
    choose = Node([Node([choose])])

start.adj.append(choose)
ans = [['N'] * Node.cnt for i in range(Node.cnt)]
def dfs(v):
    if v.seen:
        return
    v.seen = True
    for u in v.adj:
        ans[v.id][u.id] = ans[v.id][u.id] = 'Y'
        dfs(u)
dfs(start)

print(Node.cnt)
for line in ans:
    print(''.join(line))
