Problem:
Score : 1200 points

Problem Statement

Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.

On a number line, there are N copies of Takahashi, numbered 1 through N.
The i-th copy is located at position X_i and starts walking with velocity V_i in the positive direction at time 0.

Kenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else.

Kenus can select some of the copies of Takahashi at time 0, and transform them into copies of Aoki, another Ninja.
The walking velocity of a copy does not change when it transforms.
From then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki.

Among the 2^N ways to transform some copies of Takahashi into copies of Aoki at time 0, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time?
Find the count modulo 10^9+7.

Constraints

1 ≤ N ≤ 200000

1 ≤ X_i,V_i ≤ 10^9(1 ≤ i ≤ N)

X_i and V_i are integers.

All X_i are distinct.

All V_i are distinct.

Input

The input is given from Standard Input in the following format:

N
X_1 V_1
:
X_N V_N

Output

Print the number of the ways that cause all the copies of Takahashi to turn into copies of Aoki after a sufficiently long time, modulo 10^9+7.

Sample Input 1

3
2 5
6 1
3 7

Sample Output 1

6

All copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: (2), (3), (1,2), (1,3), (2,3) and (1,2,3).

Sample Input 2

4
3 7
2 9
8 16
10 8

Sample Output 2

9

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

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
using Enu = System.Linq.Enumerable;

public class Program
{
    static readonly int Mod = (int)1e9 + 7;

    public void Solve()
    {
        int N = Reader.Int();
        int[] X = new int[N], V = new int[N];
        for (int i = 0; i < N; i++) { X[i] = Reader.Int(); V[i] = Reader.Int(); }
        V = Compress(V);
        Array.Sort(X, V);
        int[] L = new int[N], R = new int[N];

        for (int i = 0, max = -1; i < N; i++)
            R[i] = max = Math.Max(max, V[i] + 1);
        for (int i = N - 1, min = int.MaxValue; i >= 0; i--)
            L[i] = min = Math.Min(min, V[i]);

        var BIT = new BinaryIndexedTree(N + 1, Mod);
        BIT.Add(0, 1);
        for (int i = 0; i < N; i++)
            BIT.Add(R[i], BIT.Sum(L[i], R[i] + 1));

        Console.WriteLine(BIT.Sum(N, N + 1));
    }

    int[] Compress<T>(T[] A)
    {
        var sortedSet = new SortedSet<T>();
        foreach (var a in A) sortedSet.Add(a);
        var sorted = sortedSet.ToArray();
        var res = new int[A.Length];
        for (int i = 0; i < A.Length; i++) res[i] = Array.BinarySearch(sorted, A[i]);
        return res;
    }
}

class BinaryIndexedTree
{
    private readonly int N;
    private readonly int Mod;
    private readonly int[] A;

    public BinaryIndexedTree(int N, int mod)
    {
        this.N = N + 1;
        Mod = mod;
        A = new int[N + 2];
    }
    public void Add(int i, int val)
    {
        if (i < 0) return;
        for (++i; i <= N; i += i & -i) ModAdd(ref A[i], val);
    }
    public int Sum(int i) // [0, i]
    {
        if (i < 0) return 0;
        int sum = 0;
        for (++i; i > 0; i &= i - 1) ModAdd(ref sum, A[i]);
        return sum;
    }
    public int Sum(int L, int R) // [L, R)
    {
        return (Sum(R - 1) - Sum(L - 1) + Mod) % Mod;
    }
    void ModAdd(ref int a, int b) { a += b; if (a >= Mod) a -= Mod; }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}