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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, &T) -> usize;
    fn upper_bound(&self, &T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for VecDeque<T>{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
impl<T: Ord> BinarySearch<T> for [T]{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

fn matmul(A:&Vec<Vec<i64>>, B:&Vec<Vec<i64>>) -> Vec<Vec<i64>>{
    let mut C = vec![vec![0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}
fn matpow(A:&mut Vec<Vec<i64>>, n:usize) -> Vec<Vec<i64>>{
    let mut B = vec![vec![0;A.len()];A.len()];
    for i in 0..A.len(){
        B[i][i] = 1;
    }
    let mut n = n;
    let mut tmp = A.clone();
    while(n>0){
        if n&1 == 1{B = matmul(&B, &tmp);}
        tmp = matmul(&tmp, &tmp);
        n>>=1;
    }
    return B;
}

 
 
 

/*
subset enumeration
let mut set;
let mut subset = set;
        for sm2 in 0..1<<n{
            if subset==0{
                break;
            }

            hogehoge


            subset = (subset-1)&set;
        }
*/
/*
全方位木
    fn dfs(s:usize,bef:usize,m:i64, g:&Vec<Vec<usize>>, dp:&mut Vec<Vec<i64>>)->i64{
        let mut res = 1;
        for i in 0..g[s].len(){
            let e = g[s][i];
            if e != bef{
                dp[s][i] = dfs(e, s, m, g, dp);
                res *= (1 + dp[s][i]);
                res %= m;
            }
        }
        return res;
    }
    let tmp = dfs(0, n, m, &g, &mut dp);
    fn dfs2(s:usize, bef:usize, p:i64, m:i64, g:&Vec<Vec<usize>>, dp:&mut Vec<Vec<i64>>){
        for i in 0..g[s].len(){
            let e = g[s][i];
            if e == bef{dp[s][i] = p;}
        }
        let mut L = vec![0;g[s].len()];
        let mut R = vec![0;g[s].len()];

        for i in 0..g[s].len(){
            L[i] = {
                let mut tmp = 1+dp[s][i];
                tmp %= m;
                if i != 0{
                    tmp *= L[i-1];
                }
                tmp%m
            }
        }

        for i in (0..g[s].len()).rev(){
            if i+1<g[s].len(){
                R[i] = (R[i+1]*((1+dp[s][i])%m))%m;
            }
            else{
                R[i] = (1+dp[s][i])%m;
            }

            if g[s][i] == bef{
                continue;
            }  
            let mut tmp = 1;
            if i != 0{
                tmp *= L[i-1];
                tmp %= m;
            }
            if i+1 != g[s].len(){
                tmp *= R[i+1];
                tmp %= m;
            }
            dfs2(g[s][i], s, tmp, m, g, dp);
        }
    }

    */
fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}
struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    size_edge:Vec<usize>,
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        UnionFind{
            par:par,
            rank:vec![0;n],
            size:vec![1;n],
            size_edge:vec![0;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
                self.size_edge[y] += self.size_edge[x];
                self.size_edge[y] += 1;
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                self.size_edge[x] += self.size_edge[y];
                self.size_edge[x] += 1;
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
            
        }
        else{
            self.size_edge[x] += 1;
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s
    }
}
pub mod FenwickTree {
    use std::ops::{AddAssign, Sub};
    pub struct FenwickTree<i64> {
        n: usize,
        data: Vec<i64>,
        init: i64,
    }
 
    impl<i64: Copy + AddAssign + Sub<Output = i64>> FenwickTree<i64> {
        pub fn new(size: usize, init: i64) -> FenwickTree<i64> {
            FenwickTree {
                n: size + 1,
                data: vec![init; size + 1],
                init: init,
            }
        }
 
        pub fn add(&mut self, k: usize, value: i64) {
            let mut x = k;
            while x < self.n {
                self.data[x] += value;
                x |= x + 1;
            }
        }
 
        /// Returns a sum of range `[l, r)`
        pub fn sum(&self, l: usize, r: usize) -> i64 {
            self.sum_one(r) - self.sum_one(l)
        }
 
        /// Returns a sum of range `[0, k)`
        pub fn sum_one(&self, k: usize) -> i64 {
            assert!(k < self.n, "k={} n={}", k, self.n);
 
            let mut result = self.init;
            let mut x = k as i32 - 1;
            while x >= 0 {
                result += self.data[x as usize];
                x = (x & (x + 1)) - 1;
            }
 
            result
        }
    }
}

pub mod FenwickTree_MOD {
    use std::ops::{AddAssign, Sub};
    use std::ops::RemAssign;
    pub struct FenwickTree<i64> {
        n: usize,
        data: Vec<i64>,
        init: i64,
        MOD:  i64,
    }
 
    impl<i64:Copy + AddAssign+ RemAssign + Sub<Output = i64>> FenwickTree<i64> {
        pub fn new(size: usize, init: i64, MOD:i64) -> FenwickTree<i64> {
            FenwickTree {
                n: size + 1,
                data: vec![init; size + 1],
                init: init,
                MOD:MOD,
            }
        }
 
        pub fn add(&mut self, k: usize, value: i64) {
            let mut x = k;
            while x < self.n {
                self.data[x] += value;
                self.data[x] %= self.MOD;
                x |= x + 1;
            }
        }
 
        /// Returns a sum of range `[l, r)`
        pub fn sum(&self, l: usize, r: usize) -> i64 {
            self.sum_one(r) - self.sum_one(l)
        }
 
        /// Returns a sum of range `[0, k)`
        pub fn sum_one(&self, k: usize) -> i64 {
            assert!(k < self.n, "k={} n={}", k, self.n);
 
            let mut result = self.init;
            let mut x = k as i32 - 1;
            while x >= 0 {
                result += self.data[x as usize];
                result %= self.MOD;
                x = (x & (x + 1)) - 1;
            }
 
            result
        }
    }
}
pub struct Scanner<R> {
    stdin: R,
}
 
impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
struct LazySegTree<BiOp> {
    n: usize,
    val: Vec<i64>,
    ma:Vec<i64>,
    op: BiOp,
    e: i64,
    upe:i64,
    inf:i64,
}

impl<BiOp> LazySegTree<BiOp>
    where BiOp: Fn(i64, i64) -> i64{
    pub fn new(n_: usize, op: BiOp, e: i64, upe:i64, inf:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2

        LazySegTree {n: n, val: vec![e; 2 * n ], ma:vec![upe;2*n], op: op, e: e, upe:upe, inf:inf}
    }
    pub fn query(&self, x:usize, y:usize, l:usize, r:usize, k:usize) -> i64 {
        if (r<=x || y<=l) {return self.inf;}
        if (x<=l && r<=y) {return self.ma[k];}
        let mut L = self.query(x,y,l,(l+r)/2, k*2);
        let mut R = self.query(x,y,(l+r)/2,r, k*2+1);
        return self.val[k] + (self.op)(L, R);

    }
    
    pub fn update(&mut self, x:usize, y:usize, v:i64, l:usize,r:usize, k:usize) {
        if (l>=r) {return;}
        if (x<=l && r<=y){
            self.val[k]+=v;
            self.ma[k]+=v;
        }
        else if(l<y && x<r){
            self.update(x, y, v, l, (l+r)/2, k*2);
            self.update(x,y,v,(l+r)/2,r, k*2+1);
            self.ma[k] = self.val[k] + (self.op)(self.ma[k*2], self.ma[k*2+1]);
        }
    }
}
fn lab(a:usize, b:usize, c:&mut usize) -> usize{
    if (b==0){return a;}
    let mut x = c.clone();
    *c = x+1;
    println!("{} {} {}", a,b,c);
    return lab(b, a%b, c);
}
fn dist_1(x0:f64, y0:f64, x1:f64, y1:f64, x2:f64, y2:f64) -> f64{
    let mut a = x2-x1;
    let mut b= y2-y1;
    let mut a2 = a*a;
    let mut b2 = b*b;
    let mut r2 = a2+b2;
    let mut tt = -(a*(x1-x0) + b*(y1-y0));
    if tt<0.0{
        return (x1 - x0)*(x1-x0) + (y1-y0)*(y1-y0);
    }
    if (tt>r2){
        return (x2-x0)*(x2-x0) + (y2-y0)*(y2-y0);
    }
    let mut f1 = a*(y1-y0)-b*(x1-x0);
    return (f1*f1)/r2;
}
fn modinv(a:usize)->usize{
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);    
    }
    u%=m;
    if u<0{u+=m;}
    return u as usize;

}
fn modpow(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%MODu;}
            x = x*x%MODu;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<usize>, ifac:&Vec<usize>)->usize{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return 1;}
        if a<b || a<0{return 0;}
        let mut tmp = ifac[a-b]*ifac[b] % MODu;
        return tmp * fac[a] % MODu;
}

fn invs()->(Vec<usize>, Vec<usize>){
    let mut ma = 1000001;
    let mut fac = vec![0;300001];
    let mut ifac = vec![0;300001];
    fac[0] = 1;
    ifac[0] = 1;
    for i in 0..300000{
        fac[i+1] = fac[i] * (i+1) % MODu;
        ifac[i+1] = ifac[i] * modpow(i+1, MODu - 2) % MODu;
    }
    (fac, ifac)
}

struct ConvexHallTrick {
    Q: Vec<(i64, i64)>,
}

impl ConvexHallTrick{
    pub fn new() -> Self {

        ConvexHallTrick {Q: Vec::new()}
    }
    pub fn calc(&self, p:(i64, i64), x:i64)->i64{
        return p.0 * x + p.1;
    }
    pub fn dodo(& self, A:(i64, i64), B:(i64, i64), C:(i64, i64)) -> bool{
        //max or min
        (A.1 - C.1) * (B.0 - A.0) <= (A.1 - B.1)*(C.0 - A.0)
    }
    pub fn add(&mut self, a:i64, b:i64){
        self.Q.push((a, b));
        let mut v = self.Q.len();
        while(v >=3 && self.dodo(self.Q[v-3], self.Q[v-2], self.Q[v-1])){
            self.Q[v-2] = self.Q[v-1];
            self.Q.pop();
            v = self.Q.len();
        }
    }
    pub fn query(& self, x:i64) -> i64{
        let mut L = -1;
        let mut R = (self.Q.len() - 1) as i64;
        while(R-L>1){
            let mut m = (L+R)/2;
            if self.calc(self.Q[m as usize], x)>=self.calc(self.Q[m as usize+1], x){
                L=m;
            }
            else{
                R=m;
            }

        }
        return self.calc(self.Q[R as usize], x);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
fn sieve(n:usize) -> (Vec<bool>, Vec<usize>){
    let mut p:usize = 0;
    let mut is_prime = vec![false; n+1];
    let mut prime = Vec::new();
    for i in 0..n+1{
        is_prime[i] = true;
    }
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n+1{
        if is_prime[i]{
            prime.push(i as usize);
            let mut j = 2*i;
            while(j<=n){
                is_prime[j] = false;
                j+=i;
            }
        }
    }
    (is_prime, prime)
    
}
fn nHr(n:usize, r:usize, fac:&Vec<usize>, ifac:&Vec<usize>) -> usize{
    comb(n + r - 1, r, fac, ifac)
}
fn gcd(a:usize, b:usize)->usize{
    if b==0{return a;}
    return gcd(b, a%b);
}
fn lcm(a:usize, b:usize)->usize{
    return (b/gcd(a, b))*a;
}
struct SegTree_MOD<BiOp> {
    n: usize,
    dat: Vec<i64>,
    op: BiOp,
    e: i64,
    mod_:i64,
}
impl<BiOp> SegTree_MOD<BiOp>
    where BiOp: Fn(i64, i64) -> i64 
          {
    pub fn new(n_: usize, op: BiOp, e: i64, mod_:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree_MOD {n: n, dat: vec![e; 2 * n - 1], op: op, e: e, mod_:mod_}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: i64) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
            self.dat[k] %= self.mod_;
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> i64 {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
                left %= self.mod_;
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
                right %= self.mod_;
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        let mut res = (self.op)(left, right);
        res %= self.mod_;
        res
        
    }
}
fn modpow2(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%13;}
            x = x*x%13;
            n = n>>1;
        }
        ans
}
#[derive(Clone)]
struct PPUnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    time:Vec<usize>,
    now:usize,
    history:Vec<(usize, usize)>,
}
impl PPUnionFind{
    fn init(n:usize) -> PPUnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        PPUnionFind{
            par:par,
            rank:vec![0;n],
            time:vec![INF as usize;n],
            now:0,
            history:vec![],
        }
    }
    fn find(&mut self, t:usize, x:usize) ->usize{
        if self.time[x] > t{return x;}
        else { let tt = self.par[x]; return self.find(t, tt);}
    }
    fn unite(&mut self, x:usize, y:usize) -> usize{
        self.now+=1;
        let mut x = x;
        let mut y = y;
        let nc = self.now;
        x = self.find(nc, x);
        y = self.find(nc, y);
        if x == y{return self.now;}
        if self.par[x] < self.par[y] {mem::swap(&mut x, &mut y);}
        self.par[x] += self.par[y];
        self.history.push((self.now, self.par[x]));
        self.par[y] = x;
        self.time[y] = self.now;
        return self.now;
    }
}

fn prim(cost:&Vec<Vec<(usize, i64)>>, vs:usize)->i64{
    let mut used = vec![false; vs];
    let mut bh = BinaryHeap::new();
    for j in 0..cost[0].len(){
            bh.push((cost[0][j].1, cost[0][j].0));
    }
    used[0] = true;
    let mut res = 0;
    while(bh.len()!=0){
        let mut m = bh.pop().unwrap();
        if used[m.1]{continue;}
        used[m.1] = true;
        for e in 0..cost[m.1].len(){
            if used[cost[m.1][e].0] == false{
                bh.push((cost[m.1][e].1, cost[m.1][e].0));
            }
        }
        res += m.0;
    }
    return res;
}
fn kruscal(cost:&mut Vec<(i64, usize, usize)>, vs:usize)->i64{
    cost.sort();
    let mut uf = UnionFind::init(vs);
    let mut res = 0;

    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res += e.0;
        }
    }
    return res;
}
fn kruscal3(cost:&mut Vec<(f64, usize, usize, usize)>, vs:usize)->(UnionFind, Vec<usize>) {
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    let mut rv = Vec::new();
    let mut c = 0.0;
    let mut t = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            rv.push(e.3);
        }
    }
    return (uf,rv);
}
fn kruscal2(cost:&mut Vec<(f64, usize, usize)>, vs:usize)->f64{
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res+= e.0;
        }
    }
    return res;
}

struct segtree<I, Op>{
    n: usize,
    dat: Vec<I>,
    op:Op,
    e:I,
}
impl<I, Op> segtree<I, Op>


    where Op: Fn(I, I) -> I, I:Copy{
        
        pub fn new(n_:usize, op: Op, e:I)->Self{
            let mut n = 1;
            while(n<n_){n*=2;}
            segtree{n: n, dat:vec![e; 2*n-1], op:op, e:e}
        }
        pub fn update(&mut self, k:usize, a:I){
            let mut k = k;
            k += self.n-1;
            self.dat[k] = a;
            while(k>0){
                k = (k-1)/2;
                self.dat[k] = (self.op)(self.dat[k*2 + 1], self.dat[k*2+2]);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> I{
            if r<=a || b<=l{return self.e;}
            if a<=l && r<=b{return self.dat[k];}
            else{
                let mut vl = self.query(a, b, k*2+1, l, (l+r)/2);
                let mut vr = self.query(a, b, k*2+2, (l+r)/2, r);
                return (self.op)(vl, vr);
            }
        }
    }
struct BIT<I, Op>{
    n:usize,
    bit:Vec<I>,
    op:Op,
    e:I,
    ini:I,
}
impl <I, Op>  BIT<I, Op>
    /* 1-index*/  
    where Op: Fn(I, I) -> I, I:Copy{
        pub fn new(n_:usize, op:Op, e:I, ini:I)->Self{
            BIT{n:n_, bit:vec![e;n_+1], op:op, e:e, ini:ini}
        }
        pub fn sum(&self, i:usize)->I{
            let mut s = self.ini;
            let mut i = i as i64;
            while(i>0){
                s = (self.op)(s, self.bit[i as usize]);
                i -= i & -i;
            }
            return s;
        }
        pub fn add(&mut self, i:usize, x:I){
            let mut i = i as i64;
            while(i<=self.n as i64){
                self.bit[i as usize] = (self.op)(self.bit[i as usize], x);
                i += i & -i;
            }
        }
    }
struct Dsegtree{
    n: usize,
    datA: Vec<i64>,
    datB:Vec<i64>,
    e:i64,
}
impl Dsegtree{
        pub fn new(n_:usize, e:i64)->Self{

            Dsegtree{n:n_, datA:vec![e; 1<<22 - 1], datB:vec![e;1<<22 - 1], e:e}
        }
        pub fn update(&mut self,a:usize, b:usize, x:i64,  k:usize, l:usize, r:usize){
            //println!("{} {} {} {} {} {}", a, b, x, k , l, r);
            if a<=l && r<=b{
                self.datA[k] += x;
            }
            else if (l<b && a<r){
                self.datB[k] += (cmp::min(b, r) as i64 - cmp::max(a, l) as i64) * x;
                self.update(a, b, x, k*2+1, l, (l+r)/2);
                self.update(a, b, x, k*2+2, (l+r)/2, r);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> i64{
            if (b<=l || r<=a){
                return 0;
            }
            else if (a<=l && r<=b){
                return self.datA[k] * ((r as i64-l as i64)) + self.datB[k];
            }
            else{
                let mut res = (cmp::min(b, r) as i64 - cmp::max(a, l) as i64)* self.datA[k];
                res += self.query(a, b, k*2+1, l, (l+r)/2);
                res += self.query(a, b, k*2+2, (l+r)/2, r);
                return res;
            }
        }
    }
/*
unwrap_or_else
*/
fn prime_factor(n:usize)->HashMap<usize, usize>{
    let mut res = HashMap::new();
    let mut n = n;
    for i in 2..n{
        if i*i>n{break;}
        while(n%i==0){
            *res.entry(i).or_insert(0)+=1;
            n/=i;
        }
    }
    if n != 1{
        res.insert(n, 1);
    }
    res
}
struct rollinghash{
    base:Vec<i64>,
    Mod:Vec<i64>,
    string:Vec<char>,
    hash:Vec<Vec<i64>>,
    power:Vec<Vec<i64>>,
}
impl rollinghash{
    pub fn new(s:&Vec<char>)->Self{
        let mut n = s.len();
        let mut base = vec![1007, 2009];
        let mut hash = vec![vec![0;n+1];2];
        let mut power = vec![vec![1;n+1];2];
        let mut Mod = vec![1000000007, 1000000009];
        for iter in 0..2{
            let mut ht = vec![0;n+1];
            let mut pt = vec![1;n+1];
            for i in 0..n{
                hash[iter][i+1] = (hash[iter][i] * base[iter] + (s[i] as usize) as i64) % Mod[iter];
                power[iter][i+1] = power[iter][i] * base[iter] % Mod[iter];
            }
        }
        return rollinghash{base:base, Mod:Mod, string:s.clone(), hash:hash, power:power}
   
    }
    pub fn get(&self, l:usize, r:usize)->(i64, i64){
        let mut res = self.hash[0][r] - self.hash[0][l] * self.power[0][r-l] % self.Mod[0];
        if res<0{
            res += self.Mod[0];
        }
        let mut res2 = self.hash[1][r] - self.hash[1][l] * self.power[1][r-l] % self.Mod[1];
        if res2<0{
            res2 += self.Mod[1];
        }
        return (res, res2);
    }

}
struct LCA{
    G:Vec<Vec<i64>>,
    parent:Vec<Vec<i64>>,
    depth:Vec<i64>,
    root:i64,
}
impl LCA{
    pub fn new(G:Vec<Vec<i64>>, N:i64,R:i64)->Self{
        let D = (f64::log2(N as f64)) as i64 + 2;
        LCA{G:G, parent:vec![vec![0;N as usize];1+D as usize], depth:vec![0;N as usize], root:R}
    }
    pub fn getP(&mut self, v:i64, p:i64, d:i64){
        self.parent[0][v as usize] = p;
        self.depth[v as usize] = d;
        for i in 0..self.G[v as usize].len(){
            if self.G[v as usize][i as usize] != p{
                let n = self.G[v as usize][i as usize];
                self.getP(n, v, d+1);
            }
        }
    }
    pub fn init(&mut self){
        let root = self.root;
        self.getP(root, -1, 0);
        let V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            for v in 0..V{
                if self.parent[k as usize][v as usize] <0{
                    self.parent[k as usize+1][v as usize] = -1;
                }
                else{
                    self.parent[k as usize+1][v as usize] = self.parent[k as usize][ (self.parent[k as usize][v as usize]) as usize];
                }
            }
        }
    }
    fn ft(&self, f:i64, d:i64)->i64{
        let mut now = f;
        let mut now2 = 0;
        let V = self.depth.len();

        let logN = f64::log2(V as f64) as i64 + 2;
        let mut v = f;
        for k in 0..logN{
            if (d >> k) & 1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }

        return v;
    }

    fn lca(&mut self,u:i64, v:i64)->i64{
        let mut u = u;
        let mut v = v;
        if self.depth[u as usize] > self.depth[v as usize]{
            mem::swap(&mut u, &mut v);
        }
        let mut V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            if ((self.depth[v as usize] - self.depth[u as usize]) >> k)&1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }
        if u == v{return u;}
        for k in (0..logN).rev(){
            if self.parent[k as usize][u as usize] != self.parent[k as usize][v as usize]{
                u = self.parent[k as usize][u as usize];
                v = self.parent[k as usize][v as usize];
            }
        }
        return self.parent[0][u as usize];
    }

    fn dist(&mut self,u:i64, v:i64)->i64{
        let lc = self.lca(u, v);
        return self.depth[u as usize] + self.depth[v as usize] - 2* self.depth[lc as usize];
    }

}
fn fast_prime_factor_talbe(ma:usize)->Vec<usize>{
    let mut p = sieve(1001);
    let mut minf = vec![0;ma];
    for j in 0..p.1.len(){
        let P = p.1[j];
        let mut now = P;
        for i in 2..ma{
            if minf[now] ==0{
                minf[now] = P;
            }
            now+=P;
            if now>=ma{
                break;
            }
        }
    }
    return minf;
}
fn area_rectanble(x1:f64, x2:f64, x3:f64, y1:f64, y2:f64, y3:f64)->f64{
    let tmp = x1*y2 + x2*y3 + x3*y1 - y1*x2 - y2*x3 - y3*x1;
    tmp.abs()/2.0
}
#[derive(PartialEq, Clone)]
struct FW(f64);

impl Eq for FW {}

impl PartialOrd for FW {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        self.0.partial_cmp(&other.0)
    }
}

impl Ord for FW {
    fn cmp(&self, other: &FW) -> Ordering {
        other.partial_cmp(self).unwrap()

    }
}
fn invs2()->(Vec<i64>, Vec<i64>){
    let mut fac = vec![0;300001];
    let mut ifac = vec![0;300001];
    fac[0] = 1;
    ifac[0] = 1;
    for i in 0..300000{
        fac[i+1] = fac[i] * (i as i64+1) % MOD;
        ifac[i+1] = ifac[i] * modpow(i+1, MODu - 2) as i64 % MOD;
    }
    (fac, ifac)
}
/* parsing
    fn expr(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = term(s, i);
        while(*i<s.len() && (s[*i] == '+' || s[*i] == '-')){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = term(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn term(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = factor(s, i);
        while(*i<s.len() && s[*i] == '*'){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = factor(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn factor(s:&Vec<char>, i:&mut usize)->Vec<usize>{
        if s[*i] == 'R' || s[*i] == 'S' || s[*i] == 'P' || s[*i] == '?'{
            let mut res = encode(s[*i]);
            *i+=1;
            return res;
        }
        *i+=1;
        let mut ret = expr(s, i);
        *i+=1;
        return ret;
    }
*/
fn matmulf64(A:&Vec<Vec<f64>>, B:&Vec<Vec<f64>>) -> Vec<Vec<f64>>{
    let mut C = vec![vec![0.0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
            }
        }
    }
    return C;
}
#[derive(Clone)]
struct edge{
    from:usize,
    to:usize,
    cost:i64,
}
struct Bellman_ford{
    es:Vec<edge>,
    d:Vec<i64>,
    V:usize,
    E:usize,
    prev:Vec<i64>
}
impl Bellman_ford{
    pub fn new(V:usize, E:usize, g:Vec<Vec<usize>>, cost:Vec<i64>)->Self{
        let mut es = vec![];
        let mut d = vec![INF; V];
        for i in 0..g.len(){
            es.push(edge{from:g[i][0], to:g[i][1], cost:cost[i]});
        }
        return Bellman_ford{V:V, E:E, d:d, es:es, prev:vec![-1;V]};
    }
    pub fn shortest_path(&mut self, s:usize){
        self.d[s] = 0;
        while(true){
            let mut update = false;
            for i in 0..self.E{
                let mut e = self.es[i].clone();
                if self.d[e.from] != INF && self.d[e.to] > self.d[e.from] + e.cost{
                    self.d[e.to] = self.d[e.from]+e.cost;
                    update = true;
                }
            }
            if !update{
                break;
            }
        }
    }
    pub fn find_negative_loop(&mut self)->bool{
        for i in 0..self.d.len(){
            self.d[i] = 0;
        }
        let mut res = false;
        for j in 0..self.V{
            for i in 0..self.E{
                let mut e = self.es[i].clone();
                if self.d[e.from] != INF && self.d[e.to] > self.d[e.from] + e.cost{
                    self.d[e.to] = self.d[e.from]+e.cost;
                    if j == self.V -1 {res = true;}
                }
            }
        }
        return res;
    }
    pub fn reproduct_shortest_path_prep(&mut self, s:usize){
        self.d = vec![INF;self.d.len()];
        self.prev = vec![-1;self.V];
        let mut used = vec![false;self.V];
        self.d[s] = 0;
        let mut cost = vec![vec![INF;self.V];self.V];
        for i in 0..self.E{
            let mut e = self.es[i].clone();
            cost[e.from][e.to] = e.cost;
        }
        while(true){
            let mut v = -1;
            for u in 0..self.V{
                if !used[u] && ( v == -1 || self.d[u] < self.d[v as usize]){v = u as i64;}
            }
            if v == -1{break;}
            used[v as usize] = true;
            for u in 0..self.V{
                if self.d[u] > self.d[v as usize] + cost[v as usize][u]{
                    self.d[u] = self.d[v as usize] + cost[v as usize][u];
                    self.prev[u] = v;
                }
            }
        }
    }
    pub fn get_path(& self,t:usize)->Vec<i64>{
        let mut path = vec![];
        let mut t = t as i64;
        while(t != -1){
            path.push(t);
            t = self.prev[t as usize];
        }
        path.reverse();
        return path;
    }
}

#[derive(PartialEq, PartialOrd)]
struct mf64(f64);
impl Eq for mf64 {}

/*
impl Ord for mf64 {
    fn cmp(&self, other: &mf64) -> Ordering {
        let ord = self.partial_cmp(other).unwrap();
        match ord {
            Ordering::Greater => Ordering::Less,
            Ordering::Less => Ordering::Greater,
            Ordering::Equal => ord
        }
    }
}
impl PartialOrd for mf64 {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
*/
impl Ord for mf64 {
    fn cmp(&self, other: &mf64) -> Ordering {
        self.partial_cmp(other).unwrap()
    }
}


fn dijkstra(s:usize, g:&Vec<Vec<(usize, i64)>>)->(Vec<usize>, Vec<i64>){
    let mut d = vec![INF;g.len()];
    let mut prev = vec![g.len();g.len()];
    d[s] = 0;
    let mut h = BinaryHeap::new();
    h.push((0, s));
    while(h.len() != 0){
        let mut top = h.pop().unwrap();
        let mut v = top.1;
        let mut l = top.0 * -1;
        if l > d[v]{
            continue;
        }
        for i in 0..g[v].len(){
            let nl = l + g[v][i].1;
            let n = g[v][i].0;
            if d[n] > nl{
                prev[n] = v;
                d[n] = nl;
                h.push((nl*-1, n));
            }
        }
    }
    (prev, d)
}
fn solve(){
    //let sssss = std::io::stdin();
    //let mut sc = Scanner { stdin: sssss.lock() };
    input!{
        N:usize,
        lr:[[usize;2];N],
    }
    let mut lr = lr.clone();
    lr.sort();
    let mut m = vec![vec![0, INF as usize];N+1];
    for i in 0..N{
        let mut v= vec![];
        v.push(lr[i].clone());
        v.push(m[i].clone());
        v.sort();
        let l = cmp::max(v[0][0], v[1][0]);
        let r = cmp::min(v[0][1], v[1][1]);
        m[i+1][0] = l;
        m[i+1][1] = r;
    }
    lr.reverse();
    let mut m2 = vec![vec![0, INF as usize];N+1];
    
    for i in 0..N{
        let mut v= vec![];
        v.push(lr[i].clone());
        v.push(m2[i].clone());
        v.sort();
        let l = cmp::max(v[0][0], v[1][0]);
        let r = cmp::min(v[0][1], v[1][1]);
        m2[i+1][0] = l;
        m2[i+1][1] = r;
    }




    m2.reverse();
    let mut res = 0;
    for i in 1..N{
        //println!("{:?} {:?}", m[i], m2[i]);
        let mut l = {if m[i][1]>=m[i][0]{m[i][1]-m[i][0]+1}else{0}};
        let mut r = {if m2[i][1]>=m2[i][0]{m2[i][1]-m2[i][0]+1}else{0}};
        res = cmp::max(res, l+r);
    }
    //println!("{:?}", m);
    //println!("{:?}", m2);
    lr.reverse();
    for i in 0..N{
        let mut l = cmp::max(m[i][0], m2[i+1][0]);
        let mut r = cmp::min(m[i][1], m2[i+1][1]);
        //println!("{:?} {} {}", lr[i], l ,r);
        res = cmp::max(res, lr[i][1] - lr[i][0]+1 + {if r>=l{r-l+1}else{0}});
    }
    println!("{}", res);

}
fn main(){
    solve();
}
const PI:f64 = std::f64::consts::PI;
pub static MOD:i64 = 1000000007;
pub static MODu:usize = 1000000007;
pub static eps:f64 = 1e-6;
const INF: i64 = 1 << 60;