Problem:
Score : 600 points

Problem Statement

10^9 contestants, numbered 1 to 10^9, will compete in a competition.
There will be two contests in this competition.

The organizer prepared N problems, numbered 1 to N, to use in these contests.
When Problem i is presented in a contest, it will be solved by all contestants from Contestant L_i to Contestant R_i (inclusive), and will not be solved by any other contestants.

The organizer will use these N problems in the two contests.
Each problem must be used in exactly one of the contests, and each contest must have at least one problem.

The joyfulness of each contest is the number of contestants who will solve all the problems in the contest.
Find the maximum possible total joyfulness of the two contests.

Constraints

2 \leq N \leq 10^5

1 \leq L_i \leq R_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 R_1
L_2 R_2
\vdots
L_N R_N

Output

Print the maximum possible total joyfulness of the two contests.

Sample Input 1

4
4 7
1 4
5 8
2 5

Sample Output 1

6

The optimal choice is:

Use Problem 1 and 3 in the first contest. Contestant 5, 6, and 7 will solve both of them, so the joyfulness of this contest is 3.

Use Problem 2 and 4 in the second contest. Contestant 2, 3, and 4 will solve both of them, so the joyfulness of this contest is 3.

The total joyfulness of these two contests is 6. We cannot make the total joyfulness greater than 6.

Sample Input 2

4
1 20
2 19
3 18
4 17

Sample Output 2

34

Sample Input 3

10
457835016 996058008
456475528 529149798
455108441 512701454
455817105 523506955
457368248 814532746
455073228 459494089
456651538 774276744
457667152 974637457
457293701 800549465
456580262 636471526

Sample Output 3

540049931

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Arrays;
import java.util.Scanner;

public class Main {
    static final Scanner sc  = new Scanner(System.in);
    static final int     MOD = (int) 1E9 + 7;
    
    public static void main(String[] args) {
        int N = nint();
        In[] in = new In[N];
        
        for (int i = 0; i < N; i++) {
            in[i] = new In(nlong(), nlong());
        }
        Arrays.sort(in, (a, b) -> Long.compare(a.l, b.l));
        
        long[] sum1 = new long[N];
        long l1 = in[0].l;
        long r1 = in[0].r;
        sum1[0] = r1 - l1 + 1;
        for (int i = 1; i < N; i++) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l1 || r1 < li)
                break;
            
            if (l1 < li)
                l1 = li;
            
            if (ri < r1)
                r1 = ri;
            
            sum1[i] = r1 - l1 + 1;
        }
        
        long[] sum2 = new long[N];
        long l2 = in[N-1].l;
        long r2 = in[N-1].r;
        sum2[N-1] = r2 - l2 + 1;
        for (int i = N-2; i >= 0; i--) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l2 || r2 < li)
                break;
            
            if (l2 < li)
                l2 = li;
            
            if (ri < r2)
                r2 = ri;
            
            sum2[i] = r2 - l2 + 1;
        }
        
        long ans = 0;
        for (int i = 0; i < N-1; i++) {
            ans = Math.max(sum1[i] + sum2[i+1], ans);
        }

        Arrays.sort(in, (a, b) -> Long.compare(b.r, a.r));
        long[] sum4 = new long[N];
        long l4 = in[0].l;
        long r4 = in[0].r;
        sum4[0] = r4 - l4 + 1;
        for (int i = 1; i < N; i++) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l4 || r4 < li)
                break;
            
            if (l4 < li)
                l4 = li;
            
            if (ri < r4)
                r4 = ri;
            
            sum4[i] = r4 - l4 + 1;
        }
        
        long[] sum3 = new long[N];
        long l3 = in[N-1].l;
        long r3 = in[N-1].r;
        sum3[N-1] = r3 - l3 + 1;
        for (int i = N-2; i >= 0; i--) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l3 || r3 < li)
                break;
            
            if (l3 < li)
                l3 = li;
            
            if (ri < r3)
                r3 = ri;
            
            sum3[i] = r3 - l3 + 1;
        }

        for (int i = 0; i < N-1; i++) {
            ans = Math.max(sum3[i] + sum4[i+1], ans);
        }

        Arrays.sort(in, (a, b) -> Long.compare(a.r - a.l, b.r - b.l));
        long[] sum41 = new long[N];
        long l41 = in[0].l;
        long r41 = in[0].r;
        sum41[0] = r41 - l41 + 1;
        for (int i = 1; i < N; i++) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l41 || r41 < li)
                break;
            
            if (l41 < li)
                l41 = li;
            
            if (ri < r41)
                r41 = ri;
            
            sum41[i] = r41 - l41 + 1;
        }
        
        long[] sum31 = new long[N];
        long l31 = in[N-1].l;
        long r31 = in[N-1].r;
        sum31[N-1] = r31 - l31 + 1;
        for (int i = N-2; i >= 0; i--) {
            long li = in[i].l;
            long ri = in[i].r;
            if (ri < l31 || r31 < li)
                break;
            
            if (l31 < li)
                l31 = li;
            
            if (ri < r31)
                r31 = ri;
            
            sum31[i] = r31 - l31 + 1;
        }

        for (int i = 0; i < N-1; i++) {
            ans = Math.max(sum31[i] + sum41[i+1], ans);
        }

        System.out.println(ans);
    }
    static class In {
        long l;
        long r;
        In(long l, long r) {
            this.l = l;
            this.r = r;
        }
        long diff() {return r - l;};
        @Override
        public String toString() {
            return "(" + l + ", " + r + ")";
        }
    }
    
    public static long sum(int[] L, int[] R, int exceptIdx) {
        int l = 0;
        int r = (int) 1E9 + 1;
        
        for (int i = 0; i < L.length; i++) {
            if (i == exceptIdx)
                continue;
            
            if (R[i] < l || r < L[i])
                return 0;
            
            if (l < L[i])
                l = L[i];
            
            if (R[i] < r)
                r = R[i];
        }
        return r - l + 1;
    }
    
    private static long sumN(int n) {
        return (long) n * (n+1) / 2;
    }
    
    private static int nint() {
        return sc.nextInt();
    }

    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }

    private static double ndouble() {
        return sc.nextDouble();
    }

    private static double[] ndoubles(int n) {
        return ndoubles(n, 0, 0);
    }

    private static double[] ndoubles(int n, int padL, int padR) {
        double[] d = new double[n + padL + padR];
        for (int i = 0; i < n; i++) {
            d[padL + i] = ndouble();
        }
        return d;
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nchars() {
        return sc.next().toCharArray();
    }

    private static char[] nchars(int padL, int padR) {
        char[] temp = sc.next().toCharArray();
        char[] ret = new char[temp.length + padL + padR];
        System.arraycopy(temp, 0, ret, padL, temp.length);
        return ret;
    }

    private static char[][] nchars2(int h, int w) {
        return nchars2(h, w, 0, 0);
    }

    private static char[][] nchars2(int h, int w, int padLU, int padRD) {
        char[][] a2 = new char[h + padLU + padRD][w + padLU + padRD];
        for (int i = 0; i < h; i++)
            System.arraycopy(nchars(), 0, a2[padLU + i], padLU, w);
        return a2;
    }

    private static long min(long... ls) {
        return Arrays.stream(ls).min().getAsLong();
    }

    private static int min(int... is) {
        return Arrays.stream(is).min().getAsInt();
    }

    private static long max(long... ls) {
        return Arrays.stream(ls).max().getAsLong();
    }

    private static int max(int... is) {
        return Arrays.stream(is).max().getAsInt();
    }

    private static long abs(long a, long b) {
        return Math.abs(a - b);
    }
}