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.lang.reflect.Array;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;

public class TaskD implements Runnable {
    PrintWriter w ;
    InputReader c;
    public void run() {
        c = new InputReader(System.in);
        w = new PrintWriter(System.out);
        int n = c.nextInt();
        if(n==1){
            w.println("YES\n2 1\n1 2");
            w.close();
            return;
        }
        if(n%2==0){
            w.println("NO");
            w.close();
            return;
        }
        ArrayList<pair> ans = new ArrayList<>();
        for(int i=1;i<n;i++){
            ans.add(new pair(0,i));
        }
        for(int i = 1;i<n;i++){
            for(int j=i+1;j<n;j++) {
                if (i % 2 == 1 && j % 2 == 0 && i + 1 == j) continue;
                ans.add(new pair(i, j));
            }
        }
        int cn = n;
        for(int i=1;i<n;i++){
            ans.add(new pair(i,cn));
        }
        cn++;
        for(int i=1;i<n;i++){
            ans.add(new pair(i,cn));
        }
        ans.add(new pair(cn-1,cn));


        w.println("Yes\n"+(2*n+4)+" "+(2*ans.size()+1));
        for(int i=0;i<ans.size();i++){
            pair pa = ans.get(i);
            w.println(pa.x+1+" "+(pa.y+1));
        }
        int las = n+2;
        w.println(1+" "+(las+1));
        for(int i=0;i<ans.size();i++){
            pair pa = ans.get(i);
            w.println((pa.x+las+1)+" "+(pa.y+las+1));
        }
        w.close();
    }
    class pair{
        int x,y;
        pair(int a,int b){
            x = a;
            y = b;
        }
    }
    public static void sortbyColumn(int arr[][], int col){

        Arrays.sort(arr, new Comparator<int[]>()
        {
            public int compare(int[] o1, int[] o2){
                return (Integer.valueOf(o1[col]).compareTo(o2[col]));
            }
        });

    }
    static long gcd(long a, long b)    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    public static class DJSet {
        public int[] upper;

        public DJSet(int n) {
            upper = new int[n];
            Arrays.fill(upper, -1);
        }

        public int root(int x) {
            return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
        }

        public boolean equiv(int x, int y) {
            return root(x) == root(y);
        }

        public boolean union(int x, int y) {
            x = root(x);
            y = root(y);
            if (x != y) {
                if (upper[y] < upper[x]) {
                    int d = x;
                    x = y;
                    y = d;
                }
                upper[x] += upper[y];
                upper[y] = x;
            }
            return x == y;
        }
    }
    public static int[] radixSort(int[] f)    {
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        {
            int[] b = new int[65537];
            for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
            for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
            for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
            int[] d = f; f = to;to = d;
        }
        return f;
    }
    public void printArray(int[] a,int x){
        for(int i=0;i<a.length;i++)
            w.print((a[i]+x)+" ");
        w.println();
    }
    public int[] scanArrayI(int n){
        int a[] = new int[n];
        for(int i=0;i<n;i++)
            a[i] = c.nextInt();
        return a;
    }
    public long[] scanArrayL(int n){
        long a[] = new long[n];
        for(int i=0;i<n;i++)
            a[i] = c.nextLong();
        return a;
    }
    public void printArray(long[] a,long x) {
        for(int i=0;i<a.length;i++)
            w.print((a[i]+x)+" ");
        w.println();
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new TaskD(),"TaskD",1<<26).start();
    }
}