A9300 | Fox and Minimal path

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 $k$ ( $1<=k<=10^{9}$ ).

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.