You are given an integer $n$. Determine if there is an unconnected graph with $n$ vertices that contains at least two connected components and contains the number of edges that is equal to the number of vertices. Each vertex must follow one of these conditions:

1. Its degree is less than or equal to 1.
2. It's a cut-vertex.

Note

• The graph must be simple.
• Loops and multiple edges are not allowed.

Input format

• First line: $n$

Output format

Print Yes if it is an unconnected graph. Otherwise, print No.

Constraints

$1\le n\le100$