Problem:
Score : 800 points

Problem Statement

Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N).
Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence.
Then, perform the following operation until p becomes empty:

Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.

When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

N is an even number.

2 ≤ N ≤ 2 × 10^5

p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print the lexicographically smallest permutation, with spaces in between.

Sample Input 1

4
3 2 4 1

Sample Output 1

3 1 2 4

The solution above is obtained as follows:

p

q

(3, 2, 4, 1)

()

↓

↓

(3, 1)

(2, 4)

↓

↓

()

(3, 1, 2, 4)

Sample Input 2

2
1 2

Sample Output 2

1 2

Sample Input 3

8
4 6 3 2 8 5 7 1

Sample Output 3

3 1 2 7 4 6 8 5

The solution above is obtained as follows:

p

q

(4, 6, 3, 2, 8, 5, 7, 1)

()

↓

↓

(4, 6, 3, 2, 7, 1)

(8, 5)

↓

↓

(3, 2, 7, 1)

(4, 6, 8, 5)

↓

↓

(3, 1)

(2, 7, 4, 6, 8, 5)

↓

↓

()

(3, 1, 2, 7, 4, 6, 8, 5)

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)



using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;
//using System.Numerics;

class Program
{
    static void Main()
    {
        //SetIn(new StreamReader("in2.txt"));
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";

    int N;
    int[] P, A, B;
    List<string> G;
    RMQ R, L;
    void calc(int a, int b, int depth, int n)
    {
        //if (depth < 3) WriteLine(a + " " + b + " " + depth);
        if (b == a) return;
        int max = (a % 2 == 0) ? R.query(a, b, 0, 0, n) : L.query(a, b, 0, 0, n);
        int s = B[max];
        int right = ((s + 1) % 2 == 0) ? R.query(s + 1, b, 0, 0, n) : L.query(s + 1, b, 0, 0, n);
        //WriteLine(max + " " + s + " " + right);
        int t = B[right];
        G.Add($"{depth}{max} {right}");
        //WriteLine(max + " " + depth);
        calc(a, s, depth + 1, n);
        calc(s + 1, t, depth + 1, n);
        calc(t + 1, b, depth + 1, n);

    }

    void Solve()
    {
        N = cin.Nextint;
        P = cin.Scanint;
        B = new int[200001];
        for (int i = 0; i < N; i++)
        {
            B[P[i]] = i;
        }

        int n = 1;
        while (n < N) n *= 2;
        R = new RMQ(n);
        L = new RMQ(n);
        for (int i = 0; i < N; i++)
        {
            if (i % 2 == 0)
            {
                R.update(i, P[i]);
            }
            else
            {
                L.update(i, P[i]);
            }
        }
        G = new List<string>();
        calc(0, N, 0, n);
        G.Sort();
        for (int i = 0; i < G.Count; i++)
        {
            for (int j = 1; j < G[i].Length; j++)
            {
                Write(G[i][j]);
            }
            Write(" ");
        }
        WriteLine();
    }

}
class RMQ
{
    internal int n;
    internal int[] dat;

    public RMQ(int t)
    {
        n = t;
        dat = new int[2 * n - 1];
        for (int i = 0; i < 2 * n - 1; i++)
        {
            dat[i] = int.MaxValue;
        }
    }

    public void update(int k, int a)
    {
        k += n - 1;
        dat[k] = a;
        while (k > 0)
        {
            k = (k - 1) / 2;
            dat[k] = Math.Min(dat[k * 2 + 1], dat[k * 2 + 2]);
        }
    }

    public int query(int a, int b, int k, int l, int r)
    {
        if (r <= a || b <= l) return int.MaxValue;

        if (a <= l && r <= b) return dat[k];
        else
        {
            int vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
            int vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
            return Math.Min(vl, vr);
        }
    }
}
class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}