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

\(1\le n\le100\)