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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cfloat>
#include <complex>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits.h>
#include <list>
#include <map>
#include <math.h>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <time.h>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)
#define int long long
#define ll long long
#define eps LDBL_EPSILON
#define mod (ll)998244353
#define INF LLONG_MAX/10
#define P pair<int,int>
#define prique priority_queue
using namespace std;
int gcd(int a, int b) {
	if (!b)return a;
	return gcd(b, a % b);
}
int lcm(int a, int b) {
	return a / gcd(a, b) * b;
}
int mypow(int a, int b) {
	if (!b)return 1;
	if (b % 2)return mypow(a, b - 1) * a;
	int memo = mypow(a, b / 2);
	return memo * memo;
}
int modpow(int a, int b, int m = mod) {
	if (!b)return 1;
	if (b % 2)return modpow(a, b - 1, m) * a % m;
	int memo = modpow(a, b / 2, m);
	return memo * memo % m;
}
class UnionFind {
	int* par, * rank;
	P* notparent;
	vector<P>* size;
	int opcount = 0;
public:
	UnionFind(int size) {
		par = new int[size + 1];
		rank = new int[size + 1];
		this->size = new vector<P>[size + 1];
		notparent = new P[size + 1];
		rep(i, size + 1) {
			par[i] = i;
			rank[i] = 0;
			this->size[i].push_back(make_pair(-1, 1));
			notparent[i] = make_pair(INF, i);
		}
	}
	int find(int n, int t = INF) {
		if (opcount <= t) {
			if (par[n] == n)return n;
			return par[n] = find(par[n]);
		}
		if (notparent[n].first <= t)return find(notparent[n].second, t);
		return n;
	}
	void unite(int n, int m) {
		n = find(n);
		m = find(m);
		if (n == m) {
			opcount++;
			return;
		}
		if (rank[n] < rank[m]) {
			par[n] = m;
			notparent[n] = make_pair(opcount, m);
			size[m].push_back(make_pair(opcount, size[m].back().second + size[n].back().second));
		}
		else {
			par[m] = n;
			notparent[m] = make_pair(opcount, n);
			size[n].push_back(make_pair(opcount, size[n].back().second + size[m].back().second));
			if (rank[n] == rank[m])rank[n]++;
		}
		opcount++;
	}
	bool same(int n, int m, int t = INF) {
		return find(n, t) == find(m, t);
	}
	int getsize(int n, int t = INF) {
		n = find(n, t);
		auto ite = lower_bound(size[n].begin(), size[n].end(), make_pair(t, (ll)0));
		if (ite == size[n].end())ite--;
		if (t < (*ite).first)ite--;
		return (*ite).second;
	}
};
class RollingHash {
	string s;
	int n, m, base;
	int* has;
	int mypow(int x, int y) {
		if (!y)return 1;
		if (y % 2)return this->mypow(x, y - 1) * x % m;
		int memo = this->mypow(x, y / 2);
		return memo * memo % m;
	}
public:
	RollingHash(string s, int m, int b): n(s.size()), m(m), base(b) { init(s, m, b); }
	~RollingHash() { delete[] has; }
	void init(string s, int m, int b) {
		n = s.size();
		has = new int[n];
		base = b;
		this->s = s;
		this->m = m;
		rep(i, n) {
			has[i] = (int)s[i];
			if (i)has[i] += base * has[i - 1] % m;
			has[i] %= m;
		}
	}
	int query(int a, int b) {
		assert(!(a >= b || a < 0 || n < b));
		return (has[b - 1] - this->mypow(base, b - a) * (!a ? 0 : has[a - 1]) % m + m) % m;
	}
};
template<typename T>
class LazySegTree {
	int n;
	T funce, upde;
	T* node, * lazy;
	bool* lazyflag;
	function<T(T, T)> func, upd;
	T mypow(T x,int y) {
		if (!y)return upde;
		if (y % 2)return func(mypow(x, y - 1), x);
		T memo = mypow(x, y / 2);
		return func(memo, memo);
	}
	void eval(int k, int l, int r) {
		if (lazyflag[k]) {
			node[k] = func(node[k], mypow(lazy[k], r - l));
			if (r - l > 1) {
				lazy[2 * k + 1] = upd(lazy[2 * k + 1], lazy[k]);
				lazy[2 * k + 2] = upd(lazy[2 * k + 2], lazy[k]);
				lazyflag[2 * k + 1] = lazyflag[2 * k + 2] = true;
			}
			lazyflag[k] = false;
		}
	}
public:
	LazySegTree(int m, T funce, T upde, function<T(T, T)> func, function<T(T, T)> upd) : n(1), funce(funce), upde(upde), func(func), upd(upd) {
		while (n < m)n *= 2;
		node = new T[2 * n];
		lazy = new T[2 * n];
		lazyflag = new bool[2 * n];
		rep(i, 2 * n) {
			node[i] = funce;
			lazy[i] = upde;
			lazyflag[i] = false;
		}
	}
	void update(int a, int b, T x, int k = 0, int l = 0, int r = -1) {
		if (r < 0)r = n;
		eval(k, l, r);
		if (b <= l || r <= a)return;
		if (a <= l && r <= b) {
			lazy[k] = upd(lazy[k], x);
			lazyflag[k] = true;
			eval(k, l, r);
		}
		else {
			update(a, b, x, 2 * k + 1, l, (l + r) / 2);
			update(a, b, x, 2 * k + 2, (l + r) / 2, r);
			node[k] = func(node[2 * k + 1], node[2 * k + 2]);
		}
	}
	T query(int a, int b, int k = 0, int l = 0, int r = -1) {
		if (r < 0)r = n;
		eval(k, l, r);
		if (b <= l || r <= a)return funce;
		if (a <= l && r <= b)return node[k];
		T vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
		T vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
		return func(vl, vr);
	}
};
class Matrix {
	int n;
	vector<vector<int>> vec;
	void Measure() {
		rep(i, n) {
			rep(j, n) {
				if (i != j)vec[i][j] = 0;
				else vec[i][j] = 1;
			}
		}
	}
public:
	Matrix(int n) {
		this->n = n;
		vec.resize(n, vector<int>(n));
	}
	Matrix(int n, vector<int> vec) {
		if (vec.size() != n * n) {
			cerr << "Invalid construct of matrix" << endl;
			exit(1);
		}
		this->n = n;
		this->vec.resize(n, vector<int>(n));
		rep(i, n) {
			rep(j, n)this->vec[i][j] = vec[i * n + j];
		}
	}
	int operator[](int a) {
		return vec[a / n][a % n];
	}
	unsigned int size() { return n; }
	Matrix operator*(const Matrix a) {
		if (this->n != a.n) {
			cerr << "Invalid maltiply of matrix" << endl;
			exit(1);
		}
		vector<int> memo(n);
		rep(i, n) {
			rep(j, n) {
				rep(k, n) {
					memo[j] += vec[i][k] * a.vec[k][j];
				}
			}
			vec[i] = memo;
			memo.clear();
			memo.resize(n);
		}
		return *this;
	}
	Matrix letmod(int m = mod) {
		rep(i, n) {
			rep(j, n)vec[i][j] %= m;
		}
		return *this;
	}
	static Matrix measure(int n) {
		Matrix res(n);
		res.Measure();
		return res;
	}
	static Matrix mypow(Matrix a, int b, int m = mod) {
		a.letmod(m);
		if (!b)return Matrix::measure(a.size());
		if (b % 2)return (mypow(a, b - 1, m) * a).letmod(m);
		Matrix memo = mypow(a, b / 2, m);
		return (memo * memo).letmod(m);
	}
};
class mycomplex {
	double realvalue, imagvalue;
public:
	mycomplex() :realvalue(0), imagvalue(0) {}
	mycomplex(double realvalue, double imagvalue) : realvalue(realvalue), imagvalue(imagvalue) {}
	mycomplex(double realvalue) : realvalue(realvalue), imagvalue(0) {}
	mycomplex(complex<double> c) :realvalue(c.real()), imagvalue(c.imag()) {}
	mycomplex(const mycomplex& rhs) :realvalue(rhs.realvalue), imagvalue(rhs.imagvalue) {}
	double real()const { return this->realvalue; }
	double imag()const { return this->imagvalue; }
	double abs() { return hypot(realvalue, imagvalue); }
	mycomplex& operator=(const mycomplex& obj) {
		if (this != &obj) {
			this->realvalue = obj.realvalue;
			this->imagvalue = obj.imagvalue;
		}
		return *this;
	}
	mycomplex& operator=(mycomplex&& obj)noexcept {
		if (this != &obj) {
			this->realvalue = exchange(obj.realvalue, 0);
			this->imagvalue = exchange(obj.imagvalue, 0);
		}
		return *this;
	}
	mycomplex& operator+=(const mycomplex& rhs) {
		this->realvalue += rhs.realvalue;
		this->imagvalue += rhs.imagvalue;
		return *this;
	}
	friend mycomplex operator+(mycomplex lhs, const mycomplex& rhs) {
		lhs += rhs;
		return lhs;
	}
	mycomplex& operator-=(const mycomplex& rhs) {
		this->realvalue -= rhs.realvalue;
		this->imagvalue -= rhs.imagvalue;
		return *this;
	}
	mycomplex& operator-=(const double& rhs) {
		this->realvalue -= rhs;
		return *this;
	}
	friend mycomplex operator-(mycomplex lhs, const mycomplex& rhs) {
		lhs -= rhs;
		return lhs;
	}
	mycomplex& operator*=(const mycomplex& rhs) {
		double pastreal = this->realvalue;
		this->realvalue = this->realvalue * rhs.realvalue - this->imagvalue * rhs.imagvalue;
		this->imagvalue = pastreal * rhs.imagvalue + rhs.realvalue * this->imagvalue;
		return *this;
	}
	friend mycomplex operator*(mycomplex lhs, const mycomplex& rhs) {
		lhs *= rhs;
		return lhs;
	}
	mycomplex& operator/=(const mycomplex& rhs) {
		*this *= mycomplex(rhs.real(), -rhs.imag());
		double dnm = rhs.real() * rhs.real() - rhs.imag() * rhs.imag();
		this->realvalue /= dnm;
		this->imagvalue /= dnm;
		return *this;
	}
	friend mycomplex operator/(mycomplex lhs, const mycomplex& rhs) {
		lhs /= rhs;
		return lhs;
	}
};
class FastFourierTransform {
private:
	static void dft(vector<mycomplex>& func, int inverse) {
		int sz = func.size();
		if (sz == 1)return;
		vector<mycomplex> veca, vecb;
		rep(i, sz / 2) {
			veca.push_back(func[2 * i]);
			vecb.push_back(func[2 * i + 1]);
		}
		dft(veca, inverse); dft(vecb, inverse);
		mycomplex now = 1, zeta = polar(1.0, inverse * 2.0 * acos(-1) / sz);
		rep(i, sz) {
			func[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];
			now *= zeta;
		}
	}
public:
	template<typename T>
	static vector<double> multiply(vector<T> f, vector<T> g) {
		vector<mycomplex> nf, ng;
		int sz = 1;
		while (sz < f.size() + g.size())sz *= 2;
		nf.resize(sz); ng.resize(sz);
		rep(i, f.size()) {
			nf[i] = f[i];
			ng[i] = g[i];
		}
		dft(nf, 1);
		dft(ng, 1);
		rep(i, sz)nf[i] *= ng[i];
		dft(nf, -1);
		vector<double> res;
		rep(i, sz)res.push_back(nf[i].real() / sz);
		return res;
	}
};
int n;
P p[100010], a[100010], b[100010];
signed main(){
	cin >> n;
	rep(i, n)cin >> p[i].second >> p[i].first;
	sort(p, p + n);
	rep(i, n)swap(p[i].first, p[i].second);
	rep(i, n) {
		if (!i)a[i] = p[i];
		else {
			a[i].first = max(a[i - 1].first, p[i].first);
			a[i].second = a[i - 1].second;
		}
	}
	for (int i = n - 1; i >= 0; i--) {
		if (i == n - 1)b[i] = p[i];
		else {
			b[i].first = max(b[i + 1].first, p[i].first);
			b[i].second = p[i].second;
		}
	}
	int ans = 0;
	rep(i, n - 1) {
		ans = max(ans, max((int)0, a[i].second - a[i].first + 1) + max((int)0, (b[i + 1].second - b[i + 1].first + 1)));
	}
	rep(i, n) {
		ans = max(ans, p[i].second - p[i].first + 1);
		if (0 < i && i < n - 1) {
			if (a[i - 1].second < b[i + 1].first) {
				ans = max(ans, p[i].second - p[i].first + 1 - (b[i + 1].first - a[i - 1].second) + 1);
			}
		}
	}
	cout << ans << endl;
	return 0;
}