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:
//package practice;
/**
 * Created by Rajan Waliya on 02-Sep-15.
 */

import java.io.*;
import java.util.*;

//public
class D550 {

    Reader sc;
    PrintWriter out;

    void solve() throws IOException {
        int k = sc.nextInt();
        if(k%2==0){
            out.println("NO");
            return;
        }
        if(k==1){
            out.println("YES\n"+
                    "2 1\n"+
                    "1 2");
            return;
        }

        out.println("YES");
        int n = 2*k+4;
        int m=0;
        StringBuilder sb = new StringBuilder();
        // 1st node to all till 2...k
        for(int i=2;i<k+1;i++){
            sb.append(1+" "+i).append("\n");
            m++;
        }
        //to each other till k+2
        for(int i=2;i<=k;i++){
            int j=0;
            if(i%2==0){j=i+2;}
            else{j=i+1;}
            for(;j<=k+2;j++){
                sb.append(i+" "+j).append("\n");m++;
            }
        }

        sb.append((k+1)+" "+(k+2)).append("\n");m++;

        //to the other half
        sb.append(1+" "+(k+3)).append("\n");m++;

        //repeat
        for(int i=2;i<k+1;i++){
            sb.append((1+k+2)+" "+(i+k+2)).append("\n");
            m++;
        }
        for(int i=2;i<=k;i++){
            int j=0;
            if(i%2==0){j=i+2;}
            else{j=i+1;}
            for(;j<=k+2;j++){
                sb.append((i+k+2)+" "+(j+k+2)).append("\n");m++;
            }
        }
        sb.append((k+1+k+2)+" "+(k+2+k+2)).append("\n");m++;

        //now print
        out.println(n+" "+m);
        out.print(sb);
    }


    //_______congratulation!!! main logic has ended, no need to understand what is after this line.________
    void runIO() throws Exception {
        sc = new Reader();
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    public static void main(String[] args) throws Exception {
        new D550().runIO();
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10L + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.')
                while ((c = read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);
            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public String next() throws IOException {
            StringBuilder sb = new StringBuilder();
            byte c;
            while ((c = read()) <= ' ') ;
            do {
                sb.append((char) c);
            } while ((c = read()) > ' ');
            return sb.toString();
        }

        public int nextInt2() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

}