You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.

For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.

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Input

The first and the only line contain one integer n (1 ≤ n ≤ 10^5).

Output

If there is no solution, output "NO" in the first line. 

If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.

Examples

Input


3


Output


YES
1 4 5 2 3 6 

Input


4


Output


NO

Note

Example from the statement is shown for the first example. 

It can be proved that there is no solution in the second example.
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import static java.lang.Math.*;

public class code2 {
    private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private static InputReader in;
    private static PrintWriter out;
    //////////////////////////////////////////////////////////
    private static int min(int... a){int min=a[0]; for(int i:a) min=Math.min(min, i); return min;}
    private static int max(int... a){int max=a[0]; for(int i:a) max=Math.max(max, i); return max;}
    private static long min(long... a){long min=a[0]; for(long i:a)min=Math.min(min, i); return min;}
    private static long max(long... a){long max=a[0]; for(long i:a)max=Math.max(max, i); return max;}
    private static String strm(String str, long m) {
        String ans = "";
        while(m > 0) {
            if ((m&1) == 1) ans = ans.concat(str);
            str = str.concat(str); m >>= 1;
        } return ans;
    }
    private static long mod(long a, long mod) {long res = a%mod; return res>=0 ? res : res+mod;}
    private static int mod(int a, int mod) {int res = a%mod; return res>=0 ? res : res+mod;}
    private static long modpow(long x, long n, long mod) {
        x = mod(x, mod);
        long res = 1;
        while (n > 0) {
            if ((n&1) == 1) res = mod(res*x, mod);
            x = mod(x*x, mod);
            n >>= 1;
        } return res;
    }
    private static long gcd(long a, long b) {return b == 0 ? Math.abs(a) : gcd(b, a % b);}
    private static int gcd(int a, int b) {return b == 0 ? Math.abs(a) : gcd(b, a % b);}
    private static long gcd(long... a) {long gcd=a[0]; for(long x:a) gcd=gcd(gcd, x); return gcd;}
    private static int gcd(int... a) {int gcd=a[0]; for(int x:a) gcd=gcd(gcd, x); return gcd;}
    private static long lcm(long a, long b) {return Math.abs(a / gcd(a, b) * b);}
    private static boolean isEven(int num) {return ((num&1) == 0);}
    private static boolean isOdd(int num) {return !isEven(num);}
    private static boolean isEven(long num) {return ((num&1) == 0);}
    private static boolean isOdd(long num) {return !isEven(num);}
    private static class Pair<T> {
        public T x, y;
        public Pair(T x, T y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public boolean equals(Object obj) {
            if (obj == this) return true;
            if (!(obj instanceof Pair)) return false;
            Pair<T> pair = (Pair<T>)obj;
            return this.x == pair.x && this.y == pair.y;
        }
        @Override
        public String toString() {
            return ("(" + this.x + "," + this.y + ")");
        }
        @Override
        public int hashCode() {
            return (this.x+" "+this.y).hashCode();
        }
    }
    private static class Triplet<T> {
        public T x, y, z;
        public Triplet(T x, T y, T z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }
        @Override
        public boolean equals(Object obj) {
            if (obj == this) return true;
            if (!(obj instanceof Triplet)) return false;
            Triplet<T> triplet = (Triplet<T>)obj;
            return this.x == triplet.x && this.y == triplet.y && this.z == triplet.z;
        }
        @Override
        public String toString() {
            return ("(" + this.x + "," + this.y + "," + this.z + ")");
        }
        @Override
        public int hashCode() {
            return (this.x+" "+this.y+" "+this.z).hashCode();
        }
    }
    //////////////////////////////////////////////////////////
    private static final int mod = 1_000_000_007;
    private void solve() throws Exception {
        int n = in.nextInt();
        int[] arr = new int[1 + (n<<1)];
        int elements_filled = 0;
        int curr = 1;
        boolean forw = true;
        int mark1 = 1, mark2 = n+1;
        while (elements_filled < 2*n) {
            if (forw) {
                arr[mark1++] = curr;
                arr[mark2++] = curr+1;
                forw = false;
            } else {
                arr[mark2++] = curr;
                arr[mark1++] = curr+1;
                forw = true;
            }
            curr += 2;
            elements_filled += 2;
        }
        long sum_1n = 0;
        for (int i=1; i<=n; i++) sum_1n += arr[i];
        long sum = (2*(long)n*(long)n + (long)n - 1)/2;
        if (isEven((2*(long)n*(long)n + (long)n - 1)) && sum == sum_1n) {
            out.printf("%s\n", "YES");
            for (int i=1; i<=2*n; i++) out.printf("%d ", arr[i]);
        } else out.printf("%s\n", "NO");
    }
    private void run() throws Exception {
//        in = new InputReader();
//        in = new InputReader(new FileInputStream("input.txt"));
//        out = new PrintWriter(new FileWriter("output.txt"));
        in = oj ? new InputReader() : new InputReader(new FileInputStream("/home/raiden/Desktop/input.txt"));
        out = new PrintWriter(System.out, false);
//        out = new PrintWriter(new FileWriter("/home/raiden/Desktop/output.txt"), false);
        long ti = System.currentTimeMillis();
        solve(); out.flush();
        if (!oj) System.out.println("\n"+(System.currentTimeMillis()-ti)+"ms");
    }
    public static void main(String[] args) throws Exception {new code2().run();}
    //////////////////////////////////////////////////////////
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, numChars;
        private InputReader() {
            this.stream = System.in;
        }
        private InputReader(FileInputStream file) {
            this.stream = file;
        }
        private 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++];
        }

        private 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 = (res<<3) + (res<<1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private 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;
        }

        private 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 = (res<<3) + (res<<1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        private String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}
