Problem:
Score : 300 points

Problem Statement

We have N ID cards, and there are M gates.

We can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, ..., and R_i-th ID cards.

How many of the ID cards allow us to pass all the gates alone?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i \leq R_i \leq N

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M

Output

Print the number of ID cards that allow us to pass all the gates alone.

Sample Input 1

4 2
1 3
2 4

Sample Output 1

2

Two ID cards allow us to pass all the gates alone, as follows:

The first ID card does not allow us to pass the second gate.

The second ID card allows us to pass all the gates.

The third ID card allows us to pass all the gates.

The fourth ID card does not allow us to pass the first gate.

Sample Input 2

10 3
3 6
5 7
6 9

Sample Output 2

1

Sample Input 3

100000 1
1 100000

Sample Output 3

100000

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

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoderWorkspace
{
    class Program
    {
        static void Main(string[] args)
        {
            var cin = new Scanner();

            var N_IDCards = cin.nextInt();
            var M_Gates = cin.nextInt();

            int[] L = new int[M_Gates];
            int[] R = new int[M_Gates];
            for (int i = 0; i<M_Gates; i++)
            {
                L[i] = cin.nextInt();
                R[i] = cin.nextInt();
            }

            int oldL = L[0];
            int oldR = R[0];
            for(int i = 1; i < M_Gates; i++)
            {
                var a = oldL;
                var b = oldR;
                var c = L[i];
                var d = R[i];

                if(a < c && b < d)
                {
                    oldL = c;
                    oldR = b;
                }
                else if(a >= c && b >= d)
                {
                    oldL = a;
                    oldR = d;
                }
                else if (a >= c && b < d)
                {
                    oldL = a;
                    oldR = b;
                }
                else if( a < c && b >= d)
                {
                    oldL = c;
                    oldR = d;
                }
            }

            var ans = Math.Max(0, oldR - oldL + 1);
            Console.WriteLine(ans);
        }
    }
    
    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }
}