Regular Bridge

Description:

Input:

The single line of the input contains integer k (1 ≤ k ≤ 100) — the required degree of the vertices of the regular graph.

Output:

Print "NO" (without quotes), if such graph doesn't exist.

Otherwise, print "YES" in the first line and the description of any suitable graph in the next lines.

The description of the made graph must start with numbers n and m — the number of vertices and edges respectively.

Each of the next m lines must contain two integers, a and b (1 ≤ a, b ≤ n, a ≠ b), that mean that there is an edge connecting the vertices a and b. A graph shouldn't contain multiple edges and edges that lead from a vertex to itself. A graph must be connected, the degrees of all vertices of the graph must be equal k. At least one edge of the graph must be a bridge. You can print the edges of the graph in any order. You can print the ends of each edge in any order.

The constructed graph must contain at most 10⁶ vertices and 10⁶ edges (it is guaranteed that if at least one graph that meets the requirements exists, then there also exists the graph with at most 10⁶ vertices and at most 10⁶ edges).

Sample Input:

1

Sample Output:

YES
2 1
1 2

Note:

In the sample from the statement there is a suitable graph consisting of two vertices, connected by a single edge.