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.

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.