Cowboy Vlad has a birthday today! There are n children who came to the celebration. In order to greet Vlad, the children decided to form a circle around him. Among the children who came, there are both tall and low, so if they stand in a circle arbitrarily, it may turn out, that there is a tall and low child standing next to each other, and it will be difficult for them to hold hands. Therefore, children want to stand in a circle so that the maximum difference between the growth of two neighboring children would be minimal possible.

Formally, let's number children from 1 to n in a circle order, that is, for every i child with number i will stand next to the child with number i+1, also the child with number 1 stands next to the child with number n. Then we will call the discomfort of the circle the maximum absolute difference of heights of the children, who stand next to each other.

Please help children to find out how they should reorder themselves, so that the resulting discomfort is smallest possible.

Input

The first line contains a single integer n (2 ≤ n ≤ 100) — the number of the children who came to the cowboy Vlad's birthday.

The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) denoting heights of every child.

Output

Print exactly n integers — heights of the children in the order in which they should stand in a circle. You can start printing a circle with any child.

If there are multiple possible answers, print any of them.

Examples

Input


5
2 1 1 3 2


Output


1 2 3 2 1


Input


3
30 10 20


Output


10 20 30

Note

In the first example, the discomfort of the circle is equal to 1, since the corresponding absolute differences are 1, 1, 1 and 0. Note, that sequences [2, 3, 2, 1, 1] and [3, 2, 1, 1, 2] form the same circles and differ only by the selection of the starting point.

In the second example, the discomfort of the circle is equal to 20, since the absolute difference of 10 and 30 is equal to 20.
import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class Main {
    private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private static Reader 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%2==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, int n, int mod) {
        long res = 1;
        for (long p = x; n > 0; n >>= 1, p = mod((mod(p, mod)*mod(p, mod)),  mod)) {
            if ((n & 1) != 0) res = mod(mod(res, mod) * mod(p, mod), mod);
        }
        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 class Pair {
        public int x, y;
        public Pair(int x, int 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 pair = (Pair)obj;
            return this.x == pair.x && this.y == pair.y;
        }

        @Override
        public int hashCode() {
            return (this.x+" "+this.y).hashCode();
        }
    }
    private static class Triplet {
        public int x, y, z;
        public Triplet(int x, int y, int 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 triplet = (Triplet)obj;
            return this.x == triplet.x && this.y == triplet.y && this.z == triplet.z;
        }

        @Override
        public int hashCode() {
            return (this.x+" "+this.y+" "+this.z).hashCode();
        }
    }
    ////////////////////////////////////////////////////////////////////////////////////////////////////
    static class Reader {
        private BufferedReader br;
        private StringTokenizer token;
        protected Reader(FileReader obj) {
            br = new BufferedReader(obj, 32768);
            token = null;
        }
        protected Reader() {
            br = new BufferedReader(new InputStreamReader(System.in), 32768);
            token = null;
        }
        protected String next() {
            while(token == null || !token.hasMoreTokens()) {
                try {
                    token = new StringTokenizer(br.readLine());
                } catch (Exception e) {e.printStackTrace();}
            } return token.nextToken();
        }
        protected String nextLine() {
            String str="";
            try {
                str = br.readLine();
            } catch (Exception e) {e.printStackTrace();}
            return str;
        }
        protected int nextInt() {return Integer.parseInt(next());}
        protected long nextLong() {return Long.parseLong(next());}
        protected double nextDouble() {return Double.parseDouble(next());}
        protected long[] nextLongArr(int n) {
            long[] arr = new long[n]; for(int i=0; i<n; i++) arr[i] = nextLong(); return arr;
        }
        protected int[] nextIntArr(int n) {
            int[] arr = new int[n]; for(int i=0; i<n; i++) arr[i] = nextInt(); return arr;
        }
    }
    public static final int mod = 1_000_000_007;
    private static void solve() throws Exception {
        int n = in.nextInt();
        int[] arr = in.nextIntArr(n);
        Arrays.sort(arr);
        ArrayDeque<Integer> ad = new ArrayDeque<>();
        int flag = 0;
        for (int j=n-1; j>=0; j--) {
            if (flag == 0) ad.addLast(arr[j]);
            else ad.addFirst(arr[j]);
            flag = 1^flag;
        }
        Iterator itr = ad.iterator();
        while (itr.hasNext()) out.printf("%d ", itr.next());
    }
    private static void run() throws Exception
    {
//        in = new Reader();
//        in = new Reader(new FileReader("input.txt"));
//        out = new PrintWriter(new FileWriter("output.txt"));
        in = oj ? new Reader() : new Reader(new FileReader("/home/raiden/Desktop/input.txt"));
        out = new PrintWriter(System.out);
        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 {run();}
}