Problem:
Score : 2000 points

Problem Statement

There are N cards. The two sides of each of these cards are distinguishable.
The i-th of these cards has an integer A_i printed on the front side, and another integer B_i printed on the back side.
We will call the deck of these cards X.
There are also N+1 cards of another kind.
The i-th of these cards has an integer C_i printed on the front side, and nothing is printed on the back side.
We will call this another deck of cards Y.

You will play Q rounds of a game.
Each of these rounds is played independently.
In the i-th round, you are given a new card. The two sides of this card are distinguishable.
It has an integer D_i printed on the front side, and another integer E_i printed on the back side.
A new deck of cards Z is created by adding this card to X.
Then, you are asked to form N+1 pairs of cards, each consisting of one card from Z and one card from Y.
Each card must belong to exactly one of the pairs.
Additionally, for each card from Z, you need to specify which side to use.
For each pair, the following condition must be met:

(The integer printed on the used side of the card from Z) \leq (The integer printed on the card from Y)

If it is not possible to satisfy this condition regardless of how the pairs are formed and which sides are used, the score for the round will be -1.
Otherwise, the score for the round will be the count of the cards from Z whose front side is used.

Find the maximum possible score for each round.

Constraints

All input values are integers.

1 \leq N \leq 10^5

1 \leq Q \leq 10^5

1 \leq A_i ,B_i ,C_i ,D_i ,E_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
:
A_N B_N
C_1 C_2 .. C_{N+1}
Q
D_1 E_1
D_2 E_2
:
D_Q E_Q

Output

For each round, print the maximum possible score in its own line.

Sample Input 1

3
4 1
5 3
3 1
1 2 3 4
3
5 4
4 3
2 3

Sample Output 1

0
1
2

For example, in the third round, the cards in Z are (4,1),(5,3),(3,1),(2,3).
The score of 2 can be obtained by using front, back, back and front sides of them, and pair them with the fourth, third, first and second cards in Y, respectively.
It is not possible to obtain a score of 3 or greater, and thus the answer is 2.

Sample Input 2

5
7 1
9 7
13 13
11 8
12 9
16 7 8 6 9 11
7
6 11
7 10
9 3
12 9
18 16
8 9
10 15

Sample Output 2

4
3
3
1
-1
3
2

Sample Input 3

9
89 67
37 14
6 1
42 25
61 22
23 1
63 60
93 62
14 2
67 96 26 17 1 62 56 92 13 38
11
93 97
17 93
61 57
88 62
98 29
49 1
5 1
1 77
34 1
63 27
22 66

Sample Output 3

7
9
8
7
7
9
9
10
9
7
9

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using Number = System.Int64;
//using System.Numerics;
using static System.Math;
//using static MathEx;
using P = System.Collections.Generic.KeyValuePair<int, int>;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var xs = new List<int>();
            var n = ri;
            var a = new int[n];
            var b = new int[n];
            var c = new int[n + 1];
            for (int i = 0; i < n; i++)
            {
                a[i] = ri;
                b[i] = ri;
                if (a[i] < b[i]) b[i] = a[i];
                xs.Add(a[i]); xs.Add(b[i]);
            }
            for (int i = 0; i < n + 1; i++)
            {
                c[i] = ri;
                xs.Add(c[i]);
            }
            Array.Sort(c);

            var q = ri;
            var u = new int[q];
            var v = new int[q];
            for (int i = 0; i < q; i++)
            {
                u[i] = ri;
                v[i] = ri;
                if (u[i] < v[i]) v[i] = u[i];
                xs.Add(u[i]);
                xs.Add(v[i]);
            }
            xs = xs.Distinct().ToList(); xs.Sort();
            for (int i = 0; i < n; i++)
            {
                a[i] = xs.BinarySearch(a[i]);
                b[i] = xs.BinarySearch(b[i]);
            }
            for (int i = 0; i < n + 1; i++)
                c[i] = xs.BinarySearch(c[i]);
            for (int i = 0; i < q; i++)
            {
                u[i] = xs.BinarySearch(u[i]);
                v[i] = xs.BinarySearch(v[i]);
            }
            Array.Sort(b, a);
            var ys = c.Distinct().ToList(); ys.Sort();
            var k = ys.Count;

            var max = 0;
            var G = Enumerate(k + 1, x => new List<P>());
            var D = Enumerate(k + 1, x => 100000000);
            var deq = new Deque<int>();

            //greedy matching
            {
                var s = new Set<int>();
                s.IsMultiSet = true;
                for (int i = 0; i < n + 1; i++)
                    s.Add(c[i]);
                for (int i = 0; i < k - 1; i++)
                    G[i + 1].Add(new KeyValuePair<int, int>(i, 0));
                for (int i = n - 1; i >= 0; i--)
                {
                    var p = s.LowerBound(a[i]);
                    if (p < s.Count)
                    {
                        max++;
                        //Debug.WriteLine("+1 {0} {1}", xs[a[i]], xs[s[p]]);
                        var t = ys.BinarySearch(s[p]);
                        var tt = ys.BinarySearch(b[i]);
                        if (tt < 0) tt = ~tt;
                        s.RemoveAt(p);
                        G[tt].Add(new P(t, 1));
                    }
                    else
                    {
                        p = s.LowerBound(b[i]);
                        if (p == s.Count)
                        {
                            for (int j = 0; j < q; j++)
                                IO.Printer.Out.WriteLine(-1);
                            return;
                        }
                        //Debug.WriteLine("+-0 {0} {1}", xs[a[i]], xs[s[p]]);
                        s.RemoveAt(p);
                    }
                }
                //Debug.WriteLine(max);

                var pos = ys.BinarySearch(s[0]);
                D[pos] = 0;
                deq.PushBack(pos);
            }
            //for (int i = 0; i <= k; i++) foreach (var e in G[i]) IO.Printer.Out.WriteLine("{0} {1} {2}", i, e.Key, e.Value);
            //augment
            {
                while (deq.Count > 0)
                {
                    var p = deq.PopFront();
                    Debug.WriteLine(p);
                    foreach (var e in G[p])
                    {
                        if (D[e.Key] > D[p] + e.Value)
                        {
                            D[e.Key] = D[p] + e.Value;
                            if (e.Value == 0) deq.PushFront(e.Key);
                            else deq.PushBack(e.Key);
                        }
                    }
                }
            }
            Debug.WriteLine(D.AsJoinedString());
            for (int i = 0; i < q; i++)
            {
                var pb = ys.BinarySearch(v[i]);
                var pa = ys.BinarySearch(u[i]);
                if (pb < 0) pb = ~pb;
                if (pa < 0) pa = ~pa;
                var x = max - D[pb];
                var y = max - D[pa] + 1;
                var z = Max(x, y);
                if (z < 0) IO.Printer.Out.WriteLine(-1);
                else IO.Printer.Out.WriteLine(z);
            }

        }
        //*
        int ri => sc.Integer();
        long rl => sc.Long();
        double rd => sc.Double();
        string rs => sc.Scan();
        char rc => sc.Char();

        [System.Diagnostics.Conditional("DEBUG")]
        void put(params object[] a) => Debug.WriteLine(string.Join(" ", a));
        //*/
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
    static public void Main()
    {
        var solver = new Program.Solver();
        solver.Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
        public static Printer Out { get; set; }
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
        public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
        public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
        public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
        public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n) { return enumerate(n, Char); }
        public string[] Scan(int n) { return enumerate(n, Scan); }
        public double[] Double(int n) { return enumerate(n, Double); }
        public int[] Integer(int n) { return enumerate(n, Integer); }
        public long[] Long(int n) { return enumerate(n, Long); }
    }
}
#endregion

#region Set
public class Set<T>: ICollection<T>
{
    public Set() { cmp = Comparer<T>.Default; }
    public Set(IComparer<T> comparer) { cmp = comparer; }
    public Set(Comparison<T> compare) { cmp = Comparer<T>.Create(compare); }
    AVLTree<Node> tree = new AVLTree<Node>();
    IComparer<T> cmp;

    /// <summary>
    /// 値の重複を許すならばtrue，そうでなければfalse
    /// </summary>
    public bool IsMultiSet { get; set; }
    /// <summary>
    /// コレクションのサイズ． O(1)
    /// </summary>
    public int Count { get { return tree.Count; } }

    /// <summary>
    /// 要素の追加．成功した場合true，そうでなければfalse．O(logN)
    /// </summary>
    public bool Add(T item)
    {
        var v = new Node() { Key = item };
        var lb = LowerBound(item);
        if (!IsMultiSet && UpperBound(item) != lb) return false;
        tree.Insert(v, lb);
        return true;
    }
    /// <summary>
    /// 要素の削除．成功した場合true，そうでなければfalse．O(logN)
    /// </summary>
    public bool Remove(T item)
    {
        var lb = LowerBound(item);
        var ub = UpperBound(item);
        if (ub == lb) return false;
        tree.RemoveAt(lb);
        return true;
    }
    /// <summary>
    /// 0-indexed で k 番目に小さい要素を削除．成功した場合true，そうでなければfalse．O(logN)
    /// </summary>
    public bool RemoveAt(int k)
    {
        if (k < 0 || k >= Count) return false;
        tree.RemoveAt(k);
        return true;
    }
    /// <summary>
    /// 0-indexed で k 番目に小さい要素を返す．O(logN)
    /// </summary>
    public T this[int index]
    {
        get
        {
            if (index < 0 || index >= Count) throw new IndexOutOfRangeException();
            var t = tree.Find(tree.root, index);
            return t.Key;
        }
    }
    /// <summary>
    /// 要素があるなら true，そうでなければfalse
    /// </summary>
    public bool Contains(T item) { return UpperBound(item) != LowerBound(item); }
    /// <summary>
    /// itemの値以上の要素の最小のインデックスを返す．O(logN)
    /// </summary>
    public int LowerBound(T item) { return tree.root.LowerBound(item, cmp); }
    /// <summary>
    /// itemの値より大きい要素の最小のインデックスを返す．O(logN)
    /// </summary>
    public int UpperBound(T item) { return tree.root.UpperBound(item, cmp); }
    /// <summary>
    /// O(N)でなめる
    /// </summary>
    public T[] Items
    {
        get
        {
            var ret = new T[Count];
            int ptr = 0;
            walk(tree.root, ret, ref ptr);
            return ret;
        }
    }

    public bool IsReadOnly { get { return false; } }

    void walk(Node root, T[] a, ref int ptr)
    {
        if (root.cnt == 0) return;
        walk(root.lst, a, ref ptr);
        a[ptr++] = root.Key;
        walk(root.rst, a, ref ptr);
    }

    void ICollection<T>.Add(T item) { Add(item); }
    public void Clear() { tree.root = tree.NIL; }
    public void CopyTo(T[] array, int arrayIndex) { ((ICollection<T>)Items).CopyTo(array, arrayIndex); }
    public IEnumerator<T> GetEnumerator() { return ((ICollection<T>)Items).GetEnumerator(); }

    System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() { return ((ICollection<T>)Items).GetEnumerator(); }

    class Node: AVLTreeNode<Node>, IKey<T>
    {
        public T Key { get; set; }

        public override Node Push()
        {
            return this;
        }

    }
}

#endregion

#region AVLTree
public abstract class AVLTreeNode<T>: BinaryTreeNode<T>
    where T : AVLTreeNode<T>
{
    public int rank;
    public override void Update()
    {
        cnt = 1 + lst.cnt + rst.cnt;
        rank = 1 + Math.Max(lst.rank, rst.rank);
    }
}
public class AVLTree<T>: Tree<T>
    where T : AVLTreeNode<T>, new()
{
    public override void Insert(T v, int k) { root = insert(root, v, k); NIL.cnt = 0; }

    public override void RemoveAt(int k) { root = removeat(root, k); NIL.cnt = 0; }

    T insert(T t, T v, int k)
    {
        t = t.Push();
        if (t.cnt == 0)
        {
            v.lst = v.rst = NIL;
            v.Update();
            return v;
        }
        if (t.lst.cnt >= k)
            t.lst = insert(t.lst, v, k);
        else
            t.rst = insert(t.rst, v, k - t.lst.cnt - 1);
        if (t.lst.rank - t.rst.rank == -2)
        {
            if (t.rst.lst.rank > t.rst.rst.rank) t.rst = rotR(t.rst);
            t = rotL(t);
        }
        else if (t.lst.rank - t.rst.rank == 2)
        {
            if (t.lst.lst.rank < t.lst.rst.rank) t.lst = rotL(t.lst);
            t = rotR(t);
        }
        else t.Update();

        return t;
    }
    T removeat(T t, int k)
    {
        t = t.Push();
        var cnt = t.lst.cnt;
        if (cnt < k) t.rst = removeat(t.rst, k - cnt - 1);
        else if (cnt > k) t.lst = removeat(t.lst, k);
        else
        {
            if (cnt == 0) return t.rst;
            if (t.rst.cnt == 0) return t.lst;

            var next = Find(t.lst, k - 1);
            next.lst = removeat(t.lst, k - 1);
            next.rst = t.rst;
            t = next;
        }
        if (t.lst.rank - t.rst.rank == -2)
        {
            if (t.rst.lst.rank > t.rst.rst.rank) t.rst = rotR(t.rst);
            t = rotL(t);
        }
        else if (t.lst.rank - t.rst.rank == 2)
        {
            if (t.lst.lst.rank < t.lst.rst.rank) t.lst = rotL(t.lst);
            t = rotR(t);
        }
        else t.Update();
        return t;
    }
}
#endregion
#region BinaryTree
public interface IKey<K> { K Key { get; set; } }
public abstract class BinaryTreeNode<T>
    where T : BinaryTreeNode<T>
{

    public int cnt;
    public T lst, rst;
    public abstract T Push();
    /// <summary>
    /// 各ノードは必要に応じて Update を継承して使う
    /// </summary>
    public abstract void Update();
}

public abstract class Tree<TNode>
    where TNode : BinaryTreeNode<TNode>, new()
{
    public Tree() { NIL = new TNode(); NIL.lst = NIL; NIL.rst = NIL; root = NIL; }
    public readonly TNode NIL;
    public TNode root;
    public int Count { get { return root.cnt; } }
    protected TNode rotR(TNode t)
    {
        t = t.Push();
        var l = t.lst.Push();
        t.lst = l.rst;
        l.rst = t;
        t.Update();
        l.Update();
        return l;
    }
    protected TNode rotL(TNode t)
    {
        t = t.Push();
        var r = t.rst.Push();
        t.rst = r.lst;
        r.lst = t;
        r.lst = t;
        t.Update();
        r.Update();
        return r;
    }
    public TNode Find(TNode t, int k)
    {
        t = t.Push();
        if (k < t.lst.cnt) return Find(t.lst, k);
        else if (k > t.lst.cnt) return Find(t.rst, k - t.lst.cnt - 1);
        else return t;
    }
    public abstract void Insert(TNode v, int k);
    public abstract void RemoveAt(int k);
}
public static class TreeOperation
{
    static public int LowerBound<T, K>
          (this T t, K k, IComparer<K> cmp)
          where T : BinaryTreeNode<T>, IKey<K>
    {
        if (t.cnt == 0) return 0;
        if (cmp.Compare(k, t.Key) <= 0) return LowerBound(t.lst, k, cmp);
        else return 1 + t.lst.cnt + LowerBound(t.rst, k, cmp);
    }
    static public int UpperBound<T, K>
     (this T t, K k, IComparer<K> cmp)
       where T : BinaryTreeNode<T>, IKey<K>
    {
        if (t.cnt == 0) return 0;
        if (cmp.Compare(t.Key, k) <= 0) return 1 + t.lst.cnt + UpperBound(t.rst, k, cmp);
        else return UpperBound(t.lst, k, cmp);
    }
}

#endregion

#region Deque<T>

public class Deque<T>
{
    T[] buf;
    int offset;
    int count;
    int capacity;
    public int Count { get { return count; } }
    public Deque(int cap) { buf = new T[capacity = cap]; }
    public Deque() { buf = new T[capacity = 8]; }
    public T this[int index]
    {
        get { return buf[getIndex(index)]; }
        set { buf[getIndex(index)] = value; }
    }
    private int getIndex(int index)
    {
        if (index >= capacity)
            throw new IndexOutOfRangeException("out of range");
        var ret = index + offset;
        if (ret >= capacity)
            ret -= capacity;
        return ret;
    }
    public void PushFront(T item)
    {
        if (count == capacity) Extend();
        if (--offset < 0) offset += buf.Length;
        buf[offset] = item;
        ++count;
    }
    public T PopFront()
    {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        --count;
        var ret = buf[offset++];
        if (offset >= capacity) offset -= capacity;
        return ret;
    }
    public void PushBack(T item)
    {
        if (count == capacity) Extend();
        var id = count++ + offset;
        if (id >= capacity) id -= capacity;
        buf[id] = item;
    }
    public T PopBack()
    {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        return buf[getIndex(--count)];
    }
    public void Insert(T item, int index)
    {
        if (index > count) throw new IndexOutOfRangeException();
        this.PushFront(item);
        for (int i = 0; i < index; i++)
            this[i] = this[i + 1];
        this[index] = item;
    }
    public T RemoveAt(int index)
    {
        if (index < 0 || index >= count) throw new IndexOutOfRangeException();
        var ret = this[index];
        for (int i = index; i > 0; i--)
            this[i] = this[i - 1];
        this.PopFront();
        return ret;
    }
    private void Extend()
    {
        T[] newBuffer = new T[capacity << 1];
        if (offset > capacity - count)
        {
            var len = buf.Length - offset;
            Array.Copy(buf, offset, newBuffer, 0, len);
            Array.Copy(buf, 0, newBuffer, len, count - len);
        }
        else Array.Copy(buf, offset, newBuffer, 0, count);
        buf = newBuffer;
        offset = 0;
        capacity <<= 1;
    }
    public T[] Items
    {
        get
        {
            var a = new T[count];
            for (int i = 0; i < count; i++)
                a[i] = this[i];
            return a;
        }
    }
}

#endregion