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 PYTHON3):

Solution:
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]))