Problem Statement

Among the ways to label the edges of a complete graph $G$ with $N$ vertices with positive integers, a graph satisfying the following condition is called a "good complete graph".

• There exists no path that visits all $N$ vertices exactly once and whose sequence of edge labels, in the order the edges are traversed, is non-decreasing.

Determine whether a good complete graph exists. If it exists, construct one that minimizes the maximum label assigned to an edge.

Constraints

• $2 \leq N \leq 20$

Input

The input is given from Standard Input in the following format:

N

Output

If a good complete graph does not exist, print No.

If it exists, print one as follows. Let $a_{i,j}$ be the label assigned to the undirected edge connecting vertices $i$ and $j$.

Yes
a_{1,2} a_{1,3} a_{1,4} \dots a_{1,N}
a_{2,3} a_{2,4} \dots a_{2,N}
\vdots
a_{N-1,N}

If multiple solutions exist, you may print any of them.