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: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.function.DoubleUnaryOperator;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;


public class Main {
    public static void main(String[] args) {
        StringBuilder out = new StringBuilder();
        solve(out);
        PrintWriter pw = new PrintWriter(System.out);
        pw.println(out);
        pw.flush();
        pw.close();
    }

    public static void solve(StringBuilder out) {
        int n = In.ni();
        int[] l = new int[n];
        int[] r = new int[n];
        for (int i = 0; i < n; i++) {
            l[i] = In.ni();
            r[i] = In.ni();
        }
        int[] p = IndexSort.sortDescending(l);
        int[] fm = new int[n + 1];
        fm[0] = Const.IINF;
        for (int i = 0; i < n; i++) {
            fm[i + 1] = Math.min(fm[i], r[p[i]]);
        }
        int[] bm = new int[n + 1];
        bm[n] = Const.IINF;
        for (int i = n - 1; i >= 0; i--) {
            bm[i] = Math.min(bm[i + 1], r[p[i]]);
        }
        int max = 0;
        int l1 = l[p[0]];
        for (int i = 1; i < n; i++) {
            int l2 = l[p[i]];
            int r1 = fm[i];
            int r2 = r[p[i]];
            int mr = bm[i + 1];
            int v1 = (r1 - l1 + 1) + Math.max(0, (Math.min(mr, r2) - l2 + 1));
            int v2 = Math.max(0, (Math.min(mr, r1) - l1 + 1)) + (r2 - l2 + 1);
            max = Math.max(max, Math.max(v1, v2));
        }
        out.append(max);
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class In {
    public static final FastScanner fsc = new FastScanner();

    public static int ni() {
        return fsc.nextInt();
    }

    public static int ni(final IntUnaryOperator f) {
        return f.applyAsInt(fsc.nextInt());
    }

    public static int[] ni(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, i -> fsc.nextInt());
        return a;
    }

    public static int[] ni(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, i -> ni(f));
        return a;
    }

    public static int[][] ni(final int n, final int m) {
        final int[][] a = new int[n][m];
        Arrays.setAll(a, i -> ni(m));
        return a;
    }

    public static int[][] ni(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][m];
        Arrays.setAll(a, i -> ni(m, f));
        return a;
    }

    public static long nl() {
        return fsc.nextLong();
    }

    public static long nl(final LongUnaryOperator f) {
        return f.applyAsLong(fsc.nextLong());
    }

    public static long[] nl(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, i -> fsc.nextLong());
        return a;
    }

    public static long[] nl(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, i -> nl(f));
        return a;
    }

    public static long[][] nl(final int n, final int m) {
        final long[][] a = new long[n][m];
        Arrays.setAll(a, i -> nl(m));
        return a;
    }

    public static long[][] nl(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][m];
        Arrays.setAll(a, i -> nl(m, f));
        return a;
    }

    public static char[] nc() {
        return fsc.next().toCharArray();
    }

    public static char[][] nc(final int n, final int m) {
        final char[][] c = new char[n][m];
        Arrays.setAll(c, i -> nc());
        return c;
    }

    public static double nd() {
        return fsc.nextDouble();
    }

    public static double nd(final DoubleUnaryOperator f) {
        return f.applyAsDouble(fsc.nextDouble());
    }

    public static double[] nd(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, i -> fsc.nextDouble());
        return a;
    }

    public static double[] nd(final int n, final DoubleUnaryOperator f) {
        final double[] a = new double[n];
        Arrays.setAll(a, i -> nd(f));
        return a;
    }

    public static double[][] nd(final int n, final int m) {
        final double[][] a = new double[n][m];
        Arrays.setAll(a, i -> nd(m));
        return a;
    }

    public static double[][] nd(final int n, final int m, final DoubleUnaryOperator f) {
        final double[][] a = new double[n][m];
        Arrays.setAll(a, i -> nd(m, f));
        return a;
    }

    public static String ns() {
        return fsc.next();
    }

    public static String[] ns(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, i -> ns());
        return s;
    }

    public static boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = fsc.next().toCharArray();
            for (int j = 0; j < w; j++) {
                grid[i][j] = s[j] == trueCharacter;
            }
        }
        return grid;
    }
}


final class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (final IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte()) {
            return buffer[ptr++];
        } else {
            return -1;
        }
    }

    private static boolean isPrintableChar(final int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
            ptr++;
        }
        return hasNextByte();
    }

    public String next() {
        if (!hasNext()) {
            throw new NoSuchElementException();
        }
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext()) {
            throw new NoSuchElementException();
        }
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        final long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
            throw new NumberFormatException();
        }
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}

@FunctionalInterface
interface IntComparator {
    public int compare(int i, int j);

    public default boolean eq(final int i, final int j) {
        return compare(i, j) == 0;
    }

    public default boolean ne(final int i, final int j) {
        return compare(i, j) != 0;
    }

    public default boolean gt(final int i, final int j) {
        return compare(i, j) > 0;
    }

    public default boolean ge(final int i, final int j) {
        return compare(i, j) >= 0;
    }

    public default boolean lt(final int i, final int j) {
        return compare(i, j) < 0;
    }

    public default boolean le(final int i, final int j) {
        return compare(i, j) <= 0;
    }
}


final class IndexSort {
    public static int[] sort(final int[] a) {
        final int[] index = new int[a.length];
        Arrays.setAll(index, IntUnaryOperator.identity());
        ComparativeMergeSort.sort(index, (i, j) -> a[i] - a[j]);
        return index;
    }

    public static int[] sortDescending(final int[] a) {
        final int[] index = new int[a.length];
        Arrays.setAll(index, IntUnaryOperator.identity());
        ComparativeMergeSort.sort(index, (i, j) -> a[j] - a[i]);
        return index;
    }

    public static int[] sort(final long[] a) {
        final int[] index = new int[a.length];
        Arrays.setAll(index, IntUnaryOperator.identity());
        ComparativeMergeSort.sort(index, (i, j) -> Long.compare(a[i], a[j]));
        return index;
    }

    public static int[] sortDescending(final long[] a) {
        final int[] index = new int[a.length];
        Arrays.setAll(index, IntUnaryOperator.identity());
        ComparativeMergeSort.sort(index, (i, j) -> Long.compare(a[j], a[i]));
        return index;
    }
}

@FunctionalInterface
interface LongComparator {
    public int compare(long i, long j);

    public default boolean eq(final long i, final long j) {
        return compare(i, j) == 0;
    }

    public default boolean ne(final long i, final long j) {
        return compare(i, j) != 0;
    }

    public default boolean gt(final long i, final long j) {
        return compare(i, j) > 0;
    }

    public default boolean ge(final long i, final long j) {
        return compare(i, j) >= 0;
    }

    public default boolean lt(final long i, final long j) {
        return compare(i, j) < 0;
    }

    public default boolean le(final long i, final long j) {
        return compare(i, j) <= 0;
    }
}


final class ComparativeMergeSort {
    private static int INSERTION_SORT_THRESHOLD = 60;

    public static void sort(final int[] a, final IntComparator comparator) {
        sort(a, 0, a.length, comparator);
    }

    public static void sort(final int[] a, final int begin, final int end, final IntComparator comparator) {
        for (int i = begin;;) {
            final int j = i + INSERTION_SORT_THRESHOLD;
            if (j < end) {
                ComparativeInsertionSort.sort(a, i, j, comparator);
            } else {
                ComparativeInsertionSort.sort(a, i, end, comparator);
                break;
            }
            i = j;
        }
        final int len = end - begin;
        final int[] work = new int[len];
        for (int block = INSERTION_SORT_THRESHOLD; block <= len; block <<= 1) {
            final int twoBlocks = block << 1;
            for (int from = begin, max = end - block; from < max; from += twoBlocks) {
                final int mid = from + block;
                final int to = Math.min(from + twoBlocks, end);
                System.arraycopy(a, from, work, 0, block);
                for (int i = from, wi = 0, ti = mid;; i++) {
                    if (ti == to) {
                        System.arraycopy(work, wi, a, i, block - wi);
                        break;
                    } else if (comparator.gt(work[wi], a[ti])) {
                        a[i] = a[ti++];
                    } else {
                        a[i] = work[wi++];
                        if (wi == block) {
                            break;
                        }
                    }
                }
            }
        }
    }

    public static void sort(final long[] a, final LongComparator comparator) {
        sort(a, 0, a.length, comparator);
    }

    public static void sort(final long[] a, final int begin, final int end, final LongComparator comparator) {
        for (int i = begin;;) {
            final int j = i + INSERTION_SORT_THRESHOLD;
            if (j < end) {
                ComparativeInsertionSort.sort(a, i, j, comparator);
            } else {
                ComparativeInsertionSort.sort(a, i, end, comparator);
                break;
            }
            i = j;
        }
        final int len = end - begin;
        final long[] work = new long[len];
        for (int block = INSERTION_SORT_THRESHOLD; block <= len; block <<= 1) {
            final int twoBlocks = block << 1;
            for (int from = begin, max = end - block; from < max; from += twoBlocks) {
                final int mid = from + block;
                final int to = Math.min(from + twoBlocks, end);
                System.arraycopy(a, from, work, 0, block);
                for (int i = from, wi = 0, ti = mid;; i++) {
                    if (ti == to) {
                        System.arraycopy(work, wi, a, i, block - wi);
                        break;
                    } else if (comparator.gt(work[wi], a[ti])) {
                        a[i] = a[ti++];
                    } else {
                        a[i] = work[wi++];
                        if (wi == block) {
                            break;
                        }
                    }
                }
            }
        }
    }
}

/**
 * @author https://atcoder.jp/users/suisen
 */
class Const {
    public static final long MOD7 = 1_000_000_007;
    public static final long MOD9 = 1_000_000_009;
    public static final long MOD99 = 998_244_353;

    public static final long LINF = Long.MAX_VALUE >> 2;
    public static final int IINF = Integer.MAX_VALUE >> 1;
    public static final double DINF = 1e150;

    public static final double SDELTA = 1e-12;
    public static final double DELTA = 1e-9;
    public static final double LDELTA = 1e-6;

    public static final String YES = "YES";
    public static final String NO = "NO";
    public static final String Yes = "Yes";
    public static final String No = "No";
    public static final String POSSIBLE = "POSSIBLE";
    public static final String IMPOSSIBLE = "IMPOSSIBLE";
    public static final String Possible = "Possible";
    public static final String Impossible = "Impossible";

    public static final int[] dx8 = {1, 0, -1, 0, 1, -1, -1, 1};
    public static final int[] dy8 = {0, 1, 0, -1, 1, 1, -1, -1};
    public static final int[] dx = {1, 0, -1, 0};
    public static final int[] dy = {0, 1, 0, -1};

    private Const(){}
}


final class ComparativeInsertionSort {
    public static void sort(final int[] a, final int from, final int to, final IntComparator comparator) {
        for (int i = from + 1; i < to; i++) {
            final int tmp = a[i];
            if (comparator.gt(a[i - 1], tmp)) {
                int j = i;
                do {
                    a[j] = a[j - 1];
                    j--;
                } while (j > from && comparator.gt(a[j - 1], tmp));
                a[j] = tmp;
            }
        }
    }

    public static void sort(final long[] a, final int from, final int to, final LongComparator comparator) {
        for (int i = from + 1; i < to; i++) {
            final long tmp = a[i];
            if (comparator.gt(a[i - 1], tmp)) {
                int j = i;
                do {
                    a[j] = a[j - 1];
                    j--;
                } while (j > from && comparator.gt(a[j - 1], tmp));
                a[j] = tmp;
            }
        }
    }
}