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.Linq;
using CompLib.Collections.Generic;
using CompLib.Util;

public class Program
{
    private int N;
    private int[] A, B;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        A = sc.IntArray();
        B = sc.IntArray();


        // N-1回あれば任意の順番にできる
        // swapのサイクルを2つ以上できれば可能

        var sortedByB = new int[N].Select((i, index) => index).ToArray();
        Array.Sort(sortedByB, (l, r) => B[l].CompareTo(B[r]));
        var aa = new int[N].Select((i, index) => A[sortedByB[index]]).ToArray();
        var bb = new int[N].Select((i, index) => B[sortedByB[index]]).ToArray();

        var sortedByAA = new int[N].Select((i, index) => index).ToArray();

        Array.Sort(sortedByAA, (l, r) => aa[l].CompareTo(aa[r]));

        for (int i = 0; i < N; i++)
        {
            if (aa[sortedByAA[i]] > bb[i])
            {
                Console.WriteLine("No");
                return;
            }   
        }

        int p = 0;

        for (int i = 0; i < N -1; i++)
        {
            int next = sortedByAA[p];
            if (next == 0)
            {
                Console.WriteLine("Yes");
                return;
            }

            p = next;
        }

        Console.WriteLine("No");
    }


    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Collections.Generic
{
    using System;

    public class SegmentTree<T>
    {
        // 制約に合った2の冪
        private const int N = 1 << 21;
        private T[] _array;

        private T _identity;
        private Func<T, T, T> _operation;

        public SegmentTree(Func<T, T, T> operation, T identity)
        {
            _identity = identity;
            _operation = operation;
            _array = new T[N * 2];
            for (int i = 1; i < N * 2; i++)
            {
                _array[i] = _identity;
            }
        }

        /// <summary>
        /// A[i]をnに更新 O(log N)
        /// </summary>
        /// <param name="i"></param>
        /// <param name="n"></param>
        public void Update(int i, T n)
        {
            i += N;
            _array[i] = n;
            while (i > 1)
            {
                i /= 2;
                _array[i] = _operation(_array[i * 2], _array[i * 2 + 1]);
            }
        }

        private T Query(int left, int right, int k, int l, int r)
        {
            if (r <= left || right <= l)
            {
                return _identity;
            }

            if (left <= l && r <= right)
            {
                return _array[k];
            }

            return _operation(Query(left, right, k * 2, l, (l + r) / 2),
                Query(left, right, k * 2 + 1, (l + r) / 2, r));
        }

        /// <summary>
        /// A[left] op A[left+1] ... op A[right-1]を求める
        /// </summary>
        /// <param name="left"></param>
        /// <param name="right"></param>
        /// <returns></returns>
        public T Query(int left, int right)
        {
            return Query(left, right, 1, 0, N);
        }

        public T this[int i]
        {
            set { Update(i, value); }
            get { return _array[i + N]; }
        }
    }
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}