Problem:
Score : 600 points

Problem Statement

Given are two integer sequences of N elements each: A_1,...,A_N and B_1,...,B_N.
Determine if it is possible to do the following operation at most N-2 times (possibly zero) so that, for every integer i from 1 to N, A_i \leq B_i holds:

Choose two distinct integers x and y between 1 and N (inclusive), and swap the values of A_x and A_y.

Constraints

2 \leq N \leq 10^5

1 \leq A_i,B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If the objective is achievable, print Yes; if it is not, print No.

Sample Input 1

3
1 3 2
1 2 3

Sample Output 1

Yes

We should swap the values of A_2 and A_3.

Sample Input 2

3
1 2 3
2 2 2

Sample Output 2

No

Sample Input 3

6
3 1 2 6 3 4
2 2 8 3 4 3

Sample Output 3

Yes

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void solve()
    {
        int N = cin.nextint;
        var A = cin.scanint;
        var B = cin.scanint;
        var C = new int[N];
        var D = new int[N];

        Array.Copy(A, C, N);
        Array.Copy(B, D, N);

        Array.Sort(C);
        Array.Sort(D);
        for (int i = 0; i < N; i++)
        {
            if (C[i] > D[i])
            {
                WriteLine("No");
                return;
            }
        }

        Array.Sort(B, A);
        var Q = new PriorityQueue<pair>();
        var S = new Set<pair>();
        for (int i = 0; i < N; i++)
        {
            Q.Enqueue(new pair(A[i], i));
        }

        int cnt = 0;
        int start = N;
        while (Q.Any)
        {
            var d = Q.Dequeue();
            int n = d.f;
            int u = d.s;

            if (n <= B[u])
            {
                continue;
            }
            var b = B.lower_bound(n);

            for (int i = start - 1; i >= b; i--)
            {
                S.Add(new pair(A[i], i));
            }
            var k = S.LowerBound(new pair(B[u] + 1, -1)) - 1;
            if (k < 0)
            {
                for (int i = b - 1; i >= 0; i--)
                {
                    S.Add(new pair(A[i], i));
                }
                b = 0;
            }
            k = S.LowerBound(new pair(B[u] + 1, -1)) - 1;
            if (k < 0)
            {
                WriteLine("No");
                return;
            }


            var t = S[k];

            cnt++;
            Q.Enqueue(new pair(t.f, u));
            A[u] = t.f;

            S.RemoveAt(k);
            start = b;
        }


        if (cnt > N - 2)
        {
            WriteLine("No");
            return;
        }

        WriteLine("Yes");
    }

}


class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap;
    readonly int cmp;
    public PriorityQueue(int cmp = 1) { heap = new List<T>(); this.cmp = cmp; }
    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = Count++;
        while (i > 0)
        {
            int p = (i - 1) >> 1;
            if (x.CompareTo(heap[p]) * cmp <= 0) break;
            heap[i] = heap[p]; i = p;
        }
        heap[i] = x;
    }
    public T Dequeue()
    {
        T ret = heap[0]; T x = heap[--Count];
        int i = 0;
        while ((i << 1) + 1 < Count)
        {
            int a = (i << 1) + 1; int b = (i << 1) + 2;
            if (b < Count && heap[a].CompareTo(heap[b]) * cmp < 0) a = b;
            if (x.CompareTo(heap[a]) * cmp >= 0) break;
            heap[i] = heap[a]; i = a;
        }
        heap[i] = x; heap.RemoveAt(Count);
        return ret;
    }
    public int Count { get; private set; }
    public bool Any => Count > 0;
    public T Peek => heap[0];
}

/// <OriginalAuthor>camypaper</OriginalAuthor>
class Set<T>
{
    Node root;
    readonly IComparer<T> comparer;
    readonly Node nil;
    readonly T nil_key;
    public bool IsMultiSet { get; set; }
    public Set(IComparer<T> comparer, T nil_key)
    {
        this.nil_key = nil_key;
        nil = new Node(nil_key);
        root = nil;
        this.comparer = comparer;
    }
    public Set(Comparison<T> comaprison, T nil_key = default(T)) : this(Comparer<T>.Create(comaprison), nil_key) { }
    public Set(T nil_key = default(T)) : this(Comparer<T>.Default, nil_key) { }
    public bool Add(T v)
    {
        key = v;
        return insert(ref root);
    }
    public bool Remove(T v)
    {
        key = v;
        return remove(ref root);
    }
    public T this[int index] { get { return find(root, index); } }
    public int Count { get { return root.Count; } }
    public void RemoveAt(int k)
    {
        if (k < 0 || k >= root.Count) throw new ArgumentOutOfRangeException();
        removeAt(ref root, k);
    }
    public T[] Items
    {
        get
        {
            var ret = new T[root.Count];
            var k = 0;
            walk(root, ret, ref k);
            return ret;
        }
    }
    void walk(Node t, T[] a, ref int k)
    {
        if (t.Count == 0) return;
        walk(t.lst, a, ref k);
        a[k++] = t.Key;
        walk(t.rst, a, ref k);
    }

    T key;
    bool insert(ref Node t)
    {
        if (t.Count == 0) { t = new Node(key); t.lst = t.rst = nil; t.Update(); return true; }
        var cmp = comparer.Compare(t.Key, key);
        bool res;
        if (cmp > 0)
            res = insert(ref t.lst);
        else if (cmp == 0)
        {
            if (IsMultiSet) res = insert(ref t.lst);
            else return false;
        }
        else res = insert(ref t.rst);
        balance(ref t);
        return res;
    }
    bool remove(ref Node t)
    {
        if (t.Count == 0) return false;
        var cmp = comparer.Compare(key, t.Key);
        bool ret;
        if (cmp < 0) ret = remove(ref t.lst);
        else if (cmp > 0) ret = remove(ref t.rst);
        else
        {
            ret = true;
            var k = t.lst.Count;
            if (k == 0) { t = t.rst; return true; }
            if (t.rst.Count == 0) { t = t.lst; return true; }


            t.Key = find(t.lst, k - 1);
            removeAt(ref t.lst, k - 1);
        }
        balance(ref t);
        return ret;
    }
    void removeAt(ref Node t, int k)
    {
        var cnt = t.lst.Count;
        if (cnt < k) removeAt(ref t.rst, k - cnt - 1);
        else if (cnt > k) removeAt(ref t.lst, k);
        else
        {
            if (cnt == 0) { t = t.rst; return; }
            if (t.rst.Count == 0) { t = t.lst; return; }

            t.Key = find(t.lst, k - 1);
            removeAt(ref t.lst, k - 1);
        }
        balance(ref t);
    }
    void balance(ref Node t)
    {
        var balance = t.lst.Height - t.rst.Height;
        if (balance == -2)
        {
            if (t.rst.lst.Height - t.rst.rst.Height > 0) { rotR(ref t.rst); }
            rotL(ref t);
        }
        else if (balance == 2)
        {
            if (t.lst.lst.Height - t.lst.rst.Height < 0) rotL(ref t.lst);
            rotR(ref t);
        }
        else t.Update();
    }

    T find(Node t, int k)
    {
        if (k < 0 || k > root.Count) throw new ArgumentOutOfRangeException();
        for (; ; )
        {
            if (k == t.lst.Count) return t.Key;
            else if (k < t.lst.Count) t = t.lst;
            else { k -= t.lst.Count + 1; t = t.rst; }
        }
    }
    public int LowerBound(T v)
    {
        var k = 0;
        var t = root;
        for (; ; )
        {
            if (t.Count == 0) return k;
            if (comparer.Compare(v, t.Key) <= 0) t = t.lst;
            else { k += t.lst.Count + 1; t = t.rst; }
        }
    }
    public int UpperBound(T v)
    {
        var k = 0;
        var t = root;
        for (; ; )
        {
            if (t.Count == 0) return k;
            if (comparer.Compare(t.Key, v) <= 0) { k += t.lst.Count + 1; t = t.rst; }
            else t = t.lst;
        }
    }
    public T LowerBoundValue(T v)
    {
        var t = root;
        T ret = nil_key;
        for (; ; )
        {
            if (t.Count == 0) return ret;
            if (comparer.Compare(v, t.Key) <= 0)
            {
                ret = t.Key;
                t = t.lst;
            }
            else
            {
                t = t.rst;
            }
        }
    }
    public T UpperBoundValue(T v)
    {
        var t = root;
        T ret = nil_key;
        for (; ; )
        {
            if (t.Count == 0) return ret;
            if (comparer.Compare(t.Key, v) <= 0)
            {
                t = t.rst;
            }
            else
            {
                ret = t.Key;
                t = t.lst;
            }

        }
    }
    void rotR(ref Node t)
    {
        var l = t.lst;
        t.lst = l.rst;
        l.rst = t;
        t.Update();
        l.Update();
        t = l;
    }
    void rotL(ref Node t)
    {
        var r = t.rst;
        t.rst = r.lst;
        r.lst = t;
        t.Update();
        r.Update();
        t = r;
    }

    class Node
    {
        public Node(T key)
        {
            Key = key;
        }
        public int Count { get; private set; }
        public sbyte Height { get; private set; }
        public T Key { get; set; }
        public Node lst, rst;
        public void Update()
        {
            Count = 1 + lst.Count + rst.Count;
            Height = (sbyte)(1 + Math.Max(lst.Height, rst.Height));
        }
        public override string ToString()
        {
            return string.Format("Count = {0}, Key = {1}", Count, Key);
        }
    }
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => 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 => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}