Problem: Bike is interested in permutations. A permutation of length n is an integer sequence such that each integer from 0 to (n - 1) appears exactly once in it. For example, [0, 2, 1] is a permutation of length 3 while both [0, 2, 2] and [1, 2, 3] is not.

A permutation triple of permutations of length n (a, b, c) is called a Lucky Permutation Triple if and only if <image>. The sign ai denotes the i-th element of permutation a. The modular equality described above denotes that the remainders after dividing ai + bi by n and dividing ci by n are equal.

Now, he has an integer n and wants to find a Lucky Permutation Triple. Could you please help him?

Input

The first line contains a single integer n (1 ≤ n ≤ 105).

Output

If no Lucky Permutation Triple of length n exists print -1.

Otherwise, you need to print three lines. Each line contains n space-seperated integers. The first line must contain permutation a, the second line — permutation b, the third — permutation c.

If there are multiple solutions, print any of them.

Examples

Input

5


Output

1 4 3 2 0
1 0 2 4 3
2 4 0 1 3


Input

2


Output

-1

Note

In Sample 1, the permutation triple ([1, 4, 3, 2, 0], [1, 0, 2, 4, 3], [2, 4, 0, 1, 3]) is Lucky Permutation Triple, as following holds:

  * <image>; 
  * <image>; 
  * <image>; 
  * <image>; 
  * <image>. 



In Sample 2, you can easily notice that no lucky permutation triple exists.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

public class popo {

    public static boolean prime[];
    public static ArrayList[] ad=new ArrayList[2555];
    public static ArrayList<Long> xor1,xor2;
    static int []min;
    static char [][]grid;
    static int []dx = {0,0,-1,1};
    static int []dy = {-1,1,0,0};
    static int []dx8 = {1,1,1,0,-1,-1,-1,0};
    static int []dy8 = {1,0,-1,-1,-1,0,1,1};
    static ArrayList<Point> aa;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n =in.nextInt();

        if(n%2==0)
        {
            out.println("-1");
            out.close();
            return;
        }
        for (int i=0;i<n;i++)
            out.print(i+" ");
        out.println();
        for (int i=0;i<n;i++)
           out.print(i+" ");
        out.println();
        for (int i=0;i<n;i++)
            out.print((i+i)%n+" ");
        out.println();



        out.close();
    }
    static int findTriangle(int a[], int n)
    {
        int []b = new int[n+2];

        // Finding the square of each element of array.
        for (int i = 0; i < n; i++)
            b[i] = a[i] * a[i];

        // Sort the sides of array and their squares.
        Arrays.sort(a);
        Arrays.sort(b);

        // x for acute triangles
        // y for right triangles
        // z for obtuse triangles
        int x=0,y=0,z=0;
        for (int i=0; i<n; i++)
        {
            int p = i+1;
            int q = i+1;

            for (int j=i+1; j<n; j++)
            {
                // Finding the farthest point p where
                // a^2 + b^2 >= c^2.
                while (p<n-1 && b[i]+b[j]>=b[p+1])
                    p++;

                q = Math.max(q, p);

                // Finding the farthest point q where
                // a + b > c.
                while (q<n-1 && a[i]+a[j]>a[q+1])
                    q++;

                // If point p make right triangle.
                if (b[i]+b[j]==b[p])
                {
                    // All triangle between j and p are acute
                    // triangles. So add p - j - 1 in x.
                    x += Math.max(p - j - 1, 0);

                    // Increment y by 1.
                    y++;

                    // All triangle between q and p are acute
                    // triangles. So add q - p in z.
                    z += q - p;
                }

                // If no right triangle
                else
                {
                    // All triangle between j and p are acute
                    // triangles. So add p - j in x.
                    x += Math.max(p - j, 0);

                    // All triangle between q and p are acute
                    // triangles. So add q - p in z.
                    z += q - p;
                }
            }
        }


        return z;
    }

    public static long modPow(long base, long exp, long mod) {
        base = base % mod;
        long result = 1;
        while(exp > 0)
        {
            if(exp % 2== 1)
            {
                result = (result * base) % mod;
                exp --;
            }
            else
            {
                base = (base * base) % mod;
                exp = exp >> 1;
            }

        }
        return result;
    }

    public static long mod = 1000000007, inf = 100000000000000000l;
    public static long fac[],inv[];
    public static void cal()
    {
        fac = new long[100001];
        inv = new long[100001];
        fac[0]=1;
        inv[0]=1;
        for(int i=1; i<=100000; i++)
        {
            fac[i]=(fac[i-1]*i)%mod;
            //  inv[i]=(inv[i-1]*modPow(i,mod-2,mod))%mod;

        }
    }
    public static long combination(long n, long r)
    {
        long k = (fac[(int) n]%mod*inv[(int) r]%mod)%mod;
        long p = inv[(int) (n-r)]%mod;
        long m = (k*p)%mod;
        return m;
    }


    public static class Point implements Comparable<Point> {

        long x, y;

        public Point(long start, long end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = (int) (47 * hash + this.x);
            hash = (int) (47 * hash + this.y);
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Long.compare(x, o.x);
        }
    }
    static long setbits(long i)
    {
        long count = 0;
        while (i>0)
        {
            count += i & 1;
            i >>= 1;
        }
        return count;

    }

    static ArrayList<Long> sieveOfEratosthenes(int n)
    {
        // Create a boolean array "prime[0..n]" and initialize
        // all entries it as true. A value in prime[i] will
        // finally be false if i is Not a prime, else true.


        prime=new boolean[1000001];
        for(int i=0;i<n;i++)
            prime[i] = true;

        for(long p = 2; p*p <=n; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[(int)p] == true)
            {
                // Update all multiples of p
                for(long i = p*2; i <= n; i += p) {
                    prime[(int) i] = false;
                }
            }
        }
        ArrayList<Long> aa=new ArrayList<>();
        for (long i=0;i<n;i++)
        {
            if(prime[(int)i])
                aa.add(i);
        }
        return aa;

        // Print all prime numbers
      /*  for(int i = 2; i <= n; i++)
        {
            if(prime[i] == true)
                System.out.print(i + " ");
        }
       */
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private InputReader.SpaceCharFilter filter;

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

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } 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 interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}