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.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using Number = ModInt;
//using System.Numerics;
//using static System.Math;
namespace Program {
    public class Solver {
        Random rnd = new Random(0);
        public void Solve() {
            //位置 x ，速度 v のやつに色を塗ったとき
            //速度 v 未満かつ，位置 x より大のやつらすべてに色が塗られる
            //速度 v より大かつ，位置 x 未満のやつらすべてに色が塗られる
            //すなわち，x-v の二次元平面上で右下と左上が塗られる
            //その後左上の領域にある点 (x',v') にある点は (p,q) を塗る (p>x,q<v')
            //同様に右下の領域にある点 (x',v') にある点は (p,q) を塗る (p<x,q>v')
            //結局，速度 [l,r] の点が全て塗られる
            //(ここで l は位置 x 以上にある点の速度の min,r は位置 x 以下にある点の速度の max)


            var n = ri;
            var X = new int[n];
            var V = new int[n];
            for (int i = 0; i < n; i++)
            {
                X[i] = ri; V[i] = ri;
            }
            var xs = X.ToList(); xs.Sort();
            var vs = V.ToList(); vs.Sort();
            for (int i = 0; i < n; i++)
            {
                X[i] = xs.BinarySearch(X[i]);
                V[i] = vs.BinarySearch(V[i]) + 1;
            }
            Array.Sort(X, V);
            var L = new int[n];
            var R = new int[n];
            for (int i = 0; i < n; i++)
            {
                R[i] = V[i];
                if (i > 0) R[i] = Math.Max(R[i], R[i - 1]);
            }
            for (int i = n - 1; i >= 0; i--)
            {
                L[i] = V[i];
                if (i + 1 < n) L[i] = Math.Min(L[i], L[i + 1]);
            }

            var dp = new FenwickTree(n + 50);
            for (int i = 0; i < n; i++)
            {
                if (L[i] == 1) { dp.Add(R[i], 1 + dp[1, R[i]]); }
                else dp.Add(R[i], dp[L[i] - 1, R[i]]);
            }
            Console.WriteLine(dp[n, n]);
        }
        const long INF = 1L << 60;
        static int[] dx = { -1, 0, 1, 0 };
        static int[] dy = { 0, 1, 0, -1 };
        const string URDL = "URDL";
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        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(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        try
        {
            solver.Solve();
            Console.Out.Flush();
        }
        catch { }
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    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 != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion

#region Fenwick
public class FenwickTree {
    int n;
    Number[] bit;
    int max = 1;
    public FenwickTree(int size) {
        n = size; bit = new Number[n + 1];
        while ((max << 1) <= n) max <<= 1;
    }
    public Number this[int i, int j] { get { return this[j] - this[i - 1]; } }
    public Number this[int i] { get { Number s = 0; for (; i > 0; i -= i & -i) s += bit[i]; return s; } }

    public void Add(int i, Number v) {
        if (i == 0) System.Diagnostics.Debug.Fail("BIT is 1 indexed");
        for (; i <= n; i += i & -i) bit[i] += v;
    }
    public Number[] Items {
        get {
            var ret = new Number[n + 1];
            for (int i = 0; i < ret.Length; i++)
                ret[i] = this[i, i];
            return ret;
        }
    }
}
#endregion

#region ModInt
public struct ModInt {
    public const long Mod = (int)1e9 + 7;

    public long num;
    public ModInt(long n) { num = n; }
    public override string ToString() { return num.ToString(); }
    public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
    public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
    public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
    public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }

    public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }

    public static ModInt Pow(long v, long k) {
        long ret = 1;
        for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
            if ((k & 1) == 1) ret = ret * v % Mod;
        return new ModInt(ret);
    }
    public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
}
#endregion