Problem: An undirected graph is called k-regular, if the degrees of all its vertices are equal k. An edge of a connected graph is called a bridge, if after removing it the graph is being split into two connected components.

Build a connected undirected k-regular graph containing at least one bridge, or else state that such graph doesn't exist.

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). 

Examples

Input

1


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.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;


public class Main implements Runnable {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
    
    
    static void solve() throws Exception {
        int k = nextInt();
        if (k % 2 == 0) {
            out.println("NO");
            return;
        }
        out.println("YES");
        List<Edge> a = new ArrayList<Edge>();
        final int SHIFT = 2 * k - 1;
        for (int i = 2; i <= k; ++i) {
            a.add(new Edge(1, i));
            a.add(new Edge(1 + SHIFT, i + SHIFT));
            for (int j = k + 1; j <= SHIFT; ++j) {
                a.add(new Edge(i, j));
                a.add(new Edge(i + SHIFT, j + SHIFT));
            }
        }
        for (int j = k + 1; j <= SHIFT; j += 2) {
            a.add(new Edge(j, j + 1));
            a.add(new Edge(j + SHIFT, j + 1 + SHIFT));
        }
        a.add(new Edge(1, 1 + SHIFT));
        out.println((2 * SHIFT) + " " + a.size());
        for (int i = 0; i < a.size(); ++i) {
            out.println(a.get(i).u + " " + a.get(i).v);         
        }
    }
    
    static class Edge {
        int u, v;
        
        Edge(int u, int v) {
            this.u = u;
            this.v = v;
        }
    }
    
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }
    
    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    static String nextLine() throws IOException {
        tok = new StringTokenizer("");
        return in.readLine();
    }

    static boolean hasNext() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return false;
            }
            tok = new StringTokenizer(s);
        }
        return true;
    }
    
    public static void main(String args[]) {
        new Thread(null, new Main(), "Main", 1 << 28).start();
    }
    
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //in = new BufferedReader(new FileReader("input.in"));
            //out = new PrintWriter(new FileWriter("output.out"));
            Locale.setDefault(Locale.US);
            solve();
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            java.lang.System.exit(1);
        }
    }
}