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 <stdio.h>
#include <sstream>
#include <string.h>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#include <set>
#include <cctype>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <deque>
#include <limits>
#include <iomanip>
#include <ctype.h>
#include <unordered_map>
#include <random>
#include <numeric>
#include <iostream>
#include <array>

#define _USE_MATH_DEFINES
#include <iostream>
#include <math.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, double> pld;
typedef pair<double, double> pdd;
typedef pair<double, ll> pdl;
typedef pair<int, char> pic;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef priority_queue<ll, vector<ll>, greater<ll>> llgreaterq;
typedef priority_queue<pll, vector<pll>, greater<pll>> pllgreaterq;
typedef priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> plpllgreaterq;
typedef priority_queue<vi, vector<vi>, greater<vi>> vigreaterq;
typedef priority_queue<vl, vector<vl>, greater<vl >> vlgreaterq;
template <class o, class p, class q>
using tuple3q = priority_queue<tuple<o, p, q>, vector<tuple<o, p, q>>, greater<tuple<o, p, q>>>;
template <class o, class p, class q, class r>
using tuple4q = priority_queue<tuple<o, p, q, r>, vector<tuple<o, p, q, r>>, greater<tuple<o, p, q, r>>>;
int dx[] = { -1,0,1,0 };
int dy[] = { 0,-1,0,1 };
#define bit(x,v) ((ll)x << v)
#define rep(x,n) for(ll x = 0;x < n;x++)
#define rep2(x,f,v) for(ll x=f;x<v;x++)
#define repe(v,x) for(auto v : x)
// 許容する誤差ε
#define EPS (1e-10)
// 2つのスカラーが等しいかどうか
#define EQ(a,b) (std::abs(a-b) < EPS)
// 2つのベクトルが等しいかどうか
#define EQV(a,b) ( EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()) )
#define all(a) a.begin(),a.end()
#define all0(a) memset(a,0,sizeof(a))
#define allm1(a) memset(a,-1,sizeof(a))
#define put_float(v) 	cout << fixed << setprecision(10); \
						cout << v << endl
#define put(v) cout << v << endl
#define vinsert(v,p,x) v.insert(v.begin() + p,x)
#define vsort(v) sort(all(v));
#define dup(v) v.erase(unique(all(v)),v.end())
#define ion(i,j) ((i & (1LL << j)) > 0)
#define next(i) i++;i%=2
#define Len size()
#define ull unsignd long long
#define psp(a,b) push_back(make_pair(a,b))
#define psp2(a,b) push(make_pair(a,b))
#define cini(a) a; cin >> a
#define infa(a,b) (a + b) % INF
#define infm(a,b) (a * b) % INF
#define infd(a,b) (a * modinv(b)) % INF
#define infs(a,b) (a + INF - b) % INF
#define inf(a) (a) %= INF
#define inff(a) ((a) % INF)
#define No cout << "No" << endl
#define Yes cout << "Yes" << endl
#define NO cout << "NO" << endl
#define YES cout << "YES" << endl
#define smal -INF*INF
#define big INF*INF
const ll INF = 1000000007;
const int MAX = 2000010;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < MAX; i++) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}
}

// 二項係数計算
long long COM(int n, int k) {
	if (n < k) return 0;
	if (n < 0 || k < 0) return 0;
	return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll getpow(ll b, ll x, ll md) {
	ll t = b;
	ll res = 1;
	while (x > 0)
	{
		if (x & 1) {
			res *= t;
			res %= md;
		}
		x >>= 1;
		t *= t;
		t %= md;
	}
	return res;
}
ll getpow(ll b, ll x) {

	return getpow(b, x, INF);
}
ll modinv(ll x) {
	return getpow(x, INF - 2);
}
ll gcd(ll a, ll b) {
	if (b == 0) return a;
	return gcd(b, a % b);
}

class mint {
	int md = 1000000007;
public:
	long long x;
	mint(ll x, ll md) {
		this->md = md;
		this->x = (x % md + md) % md;
	}
	mint(long long x = 0) : x((x% md + md) % md) {}
	mint operator-() const {
		return mint(-x);
	}
	mint& operator+=(const mint& a) {
		if ((x += a.x) >= md) x -= md;
		return *this;
	}
	mint& operator-=(const mint& a) {
		if ((x += md - a.x) >= md) x -= md;
		return *this;
	}
	mint& operator*=(const  mint& a) {
		(x *= a.x) %= md;
		return *this;
	}
	mint operator+(const mint& a) const {
		mint res(*this);
		return res += a;
	}
	mint operator-(const mint& a) const {
		mint res(*this);
		return res -= a;
	}
	mint operator*(const mint& a) const {
		mint res(*this);
		return res *= a;
	}
	mint pow(ll t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}
	// for prime mod
	mint inv() const {
		return pow(md - 2);
	}
	mint& operator/=(const mint& a) {
		return (*this) *= a.inv();
	}
	mint operator/(const mint& a) const {
		mint res(*this);
		return res /= a;
	}

	friend ostream& operator<<(ostream& os, const mint& m) {
		os << m.x;
		return os;
	}
};

int pr[100010];
int lank[100010];
void uini(int n) {
	for (size_t i = 0; i <= n; i++)
	{
		pr[i] = i;
		lank[i] = 1;
	}
}

int parent(int x) {
	if (x == pr[x]) return x;
	return pr[x] = parent(pr[x]);
}

int same(int x, int y) {
	return parent(x) == parent(y);
}

bool unit(int x, int y) {

	int px = parent(x);
	int py = parent(y);

	if (px == py) return false;
	if (lank[py] < lank[px]) {
		pr[py] = px;
		lank[px] += lank[py];
	}
	else {
		pr[px] = py;
		lank[py] += lank[px];
	}
	return true;
}

ll n;
int ci = 0;
struct Node {
	int key;
	int priority;
	Node* parent, * left, * right;
	Node(int key, int priority);
	Node() {}
};
Node NIL;
Node::Node(int key, int priority) : key(key), priority(priority) {
	left = &NIL;
	right = &NIL;
}
Node* root = new Node();
void cenrec(Node* k) {
	if (k->key == NIL.key) return;
	cenrec(k->left);
	cout << " " << k->key;
	cenrec(k->right);
}
void fastrec(Node* k)
{
	if (k->key == NIL.key) return;
	cout << " " << k->key;
	fastrec(k->left);
	fastrec(k->right);
}
void insert(Node* v) {
	Node* y = &NIL;
	Node* x = root;
	while (x->key != NIL.key)
	{
		y = x;
		if (v->key < x->key) {
			x = x->left;
		}
		else {
			x = x->right;
		}
	}
	v->parent = y;
	if (y->key == NIL.key) {
		root = v;
	}
	else if (v->key < y->key) {
		y->left = v;
	}
	else {
		y->right = v;
	}

}

Node* find(Node* k, ll v)
{
	if (k->key == NIL.key) return &NIL;
	if (k->key == v) return k;
	if (v < k->key) return find(k->left, v);
	return find(k->right, v);
}
void delp12(Node* x) {
	if (x->key == NIL.key)  return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key == NIL.key
		&& r->key == NIL.key) {
		if (pr->left == x) {
			pr->left = &NIL;
		}
		else pr->right = &NIL;
	}
	else if (l->key != NIL.key) {
		if (pr->left == x) {
			pr->left = l;
		}
		else pr->right = l;
		l->parent = pr;
	}
	else if (r->key != NIL.key) {
		if (pr->left == x) {
			pr->left = r;
		}
		else pr->right = r;
		r->parent = pr;
	}
}
Node* get_next(Node* k) {
	if (k->key == NIL.key) return &NIL;
	Node* res = get_next(k->left);
	if (res->key != NIL.key) return res;
	return k;
}
void del(Node* x) {

	if (x->key == NIL.key) return;
	Node* l = x->left;
	Node* r = x->right;
	Node* pr = x->parent;

	if (l->key != NIL.key && r->key != NIL.key) {
		Node* nex = get_next(r);
		x->key = nex->key;
		delp12(nex);
	}
	else {
		delp12(x);
	}
}
Node* rightRotate(Node* t) {
	Node* s = t->left;
	t->left = s->right;
	s->right = t;
	return s;
}
Node* leftRotate(Node* t) {
	Node* s = t->right;
	t->right = s->left;
	s->left = t;
	return s;
}
Node* _insert(Node* t, int key, int priority) {
	if (t->key == NIL.key) {
		return new Node(key, priority);
	}
	if (key == t->key) {
		return t;
	}

	if (key < t->key) {
		t->left = _insert(t->left, key, priority);
		if (t->priority < t->left->priority) {
			t = rightRotate(t);
		}
	}
	else {
		t->right = _insert(t->right, key, priority);
		if (t->priority < t->right->priority) {
			t = leftRotate(t);
		}
	}
	return t;
}
Node* delete1(Node* t, int key);
Node* _delete(Node* t, int key) {
	if (t->left->key == NIL.key && t->right->key == NIL.key) {
		return &NIL;
	}
	else if (t->left->key == NIL.key) {
		t = leftRotate(t);
	}
	else if (t->right->key == NIL.key) {
		t = rightRotate(t);
	}
	else
	{
		if (t->left->priority > t->right->priority) {
			t = rightRotate(t);
		}
		else
			t = leftRotate(t);
	}
	return delete1(t, key);
}
Node* delete1(Node* t, int key) {
	if (t->key == NIL.key) {
		return &NIL;
	}
	if (key < t->key) {
		t->left = delete1(t->left, key);
	}
	else if (key > t->key) {
		t->right = delete1(t->right, key);
	}
	else return _delete(t, key);
	return t;
}
int H;
int left(int i) {
	return i * 2 + 1;
}
int right(int i) {
	return i * 2 + 2;
}
class edge {
public:
	int from, to, i;
	ll val;
	edge() {}
	edge(ll to) : to(to) {}
	edge(ll to, ll i) : to(to), i(i) {}
	edge(ll from, ll to, ll val) : from(from), to(to), val(val) {}
};

class LCA {
private:
	vector<vector<edge>> v;
	vector<vector<int>> parent;
	vector<int> depth;
	void dfs(int n, int m, int d) {
		parent[0][n] = m;
		depth[n] = d;
		for (auto x : v[n]) {
			if (x.to != m) dfs(x.to, n, d + 1);
		}
	}
public:
	LCA(ll N, ll root, vector<vector<edge>>& tree) {
		v = tree;
		parent = vector<vector<int>>(21, vector<int>(N + 1, 0));
		depth = vector<int>(N + 1, 0);
		dfs(root, -1, 0);
		for (int j = 0; j + 1 < 20; j++) {
			for (int i = 1; i <= N; i++) {
				if (parent[j][i] < 0) parent[j + 1][i] = -1;
				else parent[j + 1][i] = parent[j][parent[j][i]];
			}
		}
	}
	int lca(int n, int m) {
		if (depth[n] > depth[m]) swap(n, m);
		for (int j = 0; j < 20; j++) {
			if ((depth[m] - depth[n]) >> j & 1) m = parent[j][m];
		}
		if (n == m) return n;
		for (int j = 19; j >= 0; j--) {
			if (parent[j][n] != parent[j][m]) {
				n = parent[j][n];
				m = parent[j][m];
			}
		}
		return parent[0][n];
	}
	int dep(int n) { return depth[n]; }
};
ll k;
int _rank[1010];
int temp[1010];
bool compare_sa(int i, int j) {
	if (_rank[i] != _rank[j]) return _rank[i] < _rank[j];
	else {
		int ri = i + k <= n ? _rank[i + k] : -1;
		int rj = j + k <= n ? _rank[j + k] : -1;
		return ri < rj;
	}
}
void construct_sa(string S, int* sa) {
	n = S.length();

	for (size_t i = 0; i <= n; i++)
	{
		sa[i] = i;
		_rank[i] = i < n ? S[i] : -1;
	}

	for (k = 1; k <= n; k *= 2)
	{
		sort(sa, sa + n + 1, compare_sa);

		// saはソート後の接尾辞の並びになっている、rankは元の位置のindexを保持したまま、更新されている。
		// ピンとこなかった部分
		temp[sa[0]] = 0;
		for (size_t i = 1; i <= n; i++)
		{
			temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);
		}
		for (size_t i = 0; i <= n; i++)
		{
			_rank[i] = temp[i];
		}
	}
}
bool contain(string S, int* sa, string T) {
	int a = 0, b = S.length();
	// sa は 接尾辞が辞書順に並んでいる、入っているのはその位置のインデックス
	while (b - a > 1) {
		int c = (a + b) / 2;
		if (S.compare(sa[c], T.length(), T) < 0) a = c;
		else b = c;
	}
	return S.compare(sa[b], T.length(), T) == 0;
}


#define bit(x,v) ((ll)x << v)

class BIT {

	static const int MAX_N = 500010;
public:
	BIT() { memset(bit, 0, sizeof(bit)); }
	ll bit[MAX_N + 1], n;
	ll sum(int i) {
		ll s = 0;
		while (i > 0)
		{
			s += bit[i];
			i -= i & -i;
		}
		return s;
	}

	void add(int i, int x) {
		while (i <= n)
		{
			bit[i] += x;
			i += i & -i;
		}
	}


};
struct UnionFind {
	vector<int> A;
	UnionFind(int n) : A(n, -1) {}
	int find(int x) {
		if (A[x] < 0) return x;
		return A[x] = find(A[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y) return;
		if (A[x] > A[y]) swap(x, y);
		A[x] += A[y];
		A[y] = x;
	}
	int ngroups() {
		int ans = 0;
		for (auto a : A) if (a < 0) ans++;
		return ans;
	}
};
vector<ll> getp(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {
		res.push_back(2);
		while (n % 2 == 0)n /= 2;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(i);
			while (n % i == 0)n /= i;
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<ll> getp2(ll n) {

	vector<ll> res;
	ll a = 2;
	if (n % 2 == 0) {

		while (n % 2 == 0) { n /= 2; res.push_back(2); }
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {

			while (n % i == 0) { n /= i; res.push_back(i); }
		}
	}
	if (n != 1) res.push_back(n);
	return res;
}
vector<pll> getp3(ll n) {
	vector<pll> res;
	ll a = 2;
	int si = 0;
	if (n % 2 == 0) {

		res.push_back(make_pair(2, 0));
		while (n % 2 == 0) { n /= 2; res[si].second++; }
		si++;
	}

	for (ll i = 3; i * i <= n; i += 2)
	{
		if (n % i == 0) {
			res.push_back(make_pair(i, 0));
			while (n % i == 0) { n /= i; res[si].second++; }
			si++;
		}
	}
	if (n != 1) { res.push_back(make_pair(n, 1)); }
	return res;
}

vector<ll> getDivisors(ll n) {

	vector<ll> res;
	ll a = 2;
	res.push_back(1);
	for (ll i = 2; i * i <= n; i++)
	{

		if (n % i == 0) {
			res.push_back(i);
			if (n / i != i)
				res.push_back(n / i);
		}
	}
	return res;
}

struct ve {
public:
	vector<ve> child;
	int _t = INF;
	ve(int t) :_t(t) {}
	ve(ve _left, ve _right) {
		_t = _left._t + _right._t;
		child.push_back(_left);
		child.push_back(_right);
	}
	bool operator<(const ve& t) const {
		return _t > t._t;
	}
};

vector<bool> elas(ll n) {
	vector<bool> r(n);
	fill(r.begin(), r.end(), 1);
	r[0] = 0;
	r[1] = 0;
	for (ll i = 2; i * i < n; i++)
	{
		if (!r[i]) continue;
		ll ti = i * 2;
		while (ti < n)
		{
			r[ti] = false;
			ti += i;
		}
	}
	return r;
}
bool isPrime(ll v) {
	for (ll i = 2; i * i <= v; i++)
	{
		if (v % i == 0) return false;
	}
	return true;
}


class SegTree {

public:
	const static int MAX_N = 100010;
	const static int DAT_SIZE = (1 << 18) - 1;
	int N, Q;
	int A[MAX_N];


	ll data[DAT_SIZE], datb[DAT_SIZE];
	void init(int _n) {
		N = 1;
		while (N < _n) N <<= 1;
		memset(data, 0, sizeof(data));
		memset(datb, 0, sizeof(datb));
	}
	void init(int _n, ll iv) {
		N = 1;
		while (N < _n) N <<= 1;
		rep(i, DAT_SIZE) {
			data[i] = iv;
			datb[i] = iv;
		}
	}
	void add(int a, int b, int x) {
		add(a, b + 1, x, 0, 0, N);
	}
	void add(int a, int b, int x, int k, int l, int r) {
		if (a <= l && r <= b) {
			data[k] += x;
		}
		else if (l < b && a < r) {
			datb[k] += (min(b, r) - max(a, l)) * x;
			add(a, b, x, k * 2 + 1, l, (l + r) / 2);
			add(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}

	void change(int a, int b, int x) {
		change(a, b + 1, x, 0, 0, N);
	}
	void change(int a, int b, int x, int k, int l, int r) {
		if (a <= l && r <= b) {
			data[k] = x;
		}
		else if (l < b && a < r) {
			datb[k] = x;
			change(a, b, x, k * 2 + 1, l, (l + r) / 2);
			change(a, b, x, k * 2 + 2, (l + r) / 2, r);
		}
	}

	ll sum(int a, int b) {
		return sum(a, b + 1, 0, 0, N);
	}
	ll sum(int a, int b, int k, int l, int r) {
		if (b <= l || r <= a) {
			return 0;
		}
		if (a <= l && r <= b) {
			return data[k] * (r - l) + datb[k];
		}

		ll res = (min(b, r) - max(a, l)) * data[k];
		res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
		res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
		return res;
	}
};
class Segment;
class Circle;

class Point {
public:
	double x, y;

	Point(double x = 0, double y = 0) :x(x), y(y) {}

	Point operator + (Point p) { return Point(x + p.x, y + p.y); }
	Point operator - (Point p) { return Point(x - p.x, y - p.y); }
	Point operator * (double a) { return Point(a * x, a * y); }
	Point operator / (double a) { return Point(x / a, y / a); }

	double abs() { return sqrt(norm()); }
	double norm() { return x * x + y * y; }

	bool operator < (const Point& p)const {
		return x != p.x ? x < p.x : y < p.y;
	}
	bool operator == (const Point& p) const {
		return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
	}
	static double dot(Point a, Point b) {
		return a.x * b.x + a.y * b.y;
	}
	static double cross(Point a, Point b) {
		return a.x * b.y - a.y * b.x;
	}
	static bool isOrthogonal(Point a, Point b) {
		return EQ(dot(a, b), 0.0);
	}
	static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
		return isOrthogonal(a1 - a2, b1 - b2);
	}
	static bool isOrthogonal(Segment s1, Segment s2);

	static bool isPalallel(Point a, Point b) {
		return EQ(cross(a, b), 0.0);
	}
	static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {
		return isPalallel(a1 - a2, b1 - b2);
	}
	static bool isPalallel(Segment s1, Segment s2);

	static const int COUNTER_CLOCKWISE = 1;
	static const int CLOCKWISE = -1;
	static const int ONLINE_BACK = 2;
	static const int ONLINE_FRONT = -2;
	static const int ON_SEGMENT = 0;
	static int ccw(Point p0, Point p1, Point p2) {
		// 線分はp0とp1でp2がどこにあるかを探る
		Point a = p1 - p0;
		Point b = p2 - p0;
		if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
		if (cross(a, b) < -EPS) return CLOCKWISE;
		if (dot(a, b) < -EPS) return ONLINE_BACK;
		if (a.norm() < b.norm()) return ONLINE_FRONT;
		return ON_SEGMENT;
	}

	static bool intersect(Point p1, Point p2, Point p3, Point p4) {
		return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0
			&& ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
	}
	static bool intersect(Segment s1, Segment s2);
	static Point project(Segment s, Point p);

	static Point reflect(Segment s, Point p);

	static Point getDistance(Point a, Point b) {
		return (a - b).abs();
	}

	static double getDistanceLP(Segment s, Point p);

	static double getDistanceSP(Segment s, Point p);

	static double getDistance(Segment s1, Segment s2);

	static Point getIntersection(Segment s1, Segment s2);

	static pair<Point, Point> crossPoints(Circle c, Segment s);

	static int contains(vector<Point> g, Point p) {
		int n = g.size();
		bool x = false;
		rep(i, n) {
			Point a = g[i] - p, b = g[(i + 1) % n] - p;
			// 線の上に載っているか
			if (std::abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;

			// pを基準として上下にあるか
			// または外積が正か?(→にあるか)
			if (a.y > b.y) swap(a, b);
			if (a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
		}
		return x ? 2 : 0;
	}

	static vector<Point> andrewScan(vector<Point> s) {
		vector<Point> u, l;
		if (s.size() < 3) return s;
		sort(all(s));
		u.push_back(s[0]);
		u.push_back(s[1]);
		l.push_back(s[s.size() - 1]);
		l.push_back(s[s.size() - 2]);

		for (int i = 2; i < s.size(); i++) {

			for (int _n = u.size(); _n >= 2 && ccw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {
				u.pop_back();
			}
			u.push_back(s[i]);
		}

		for (int i = s.size() - 3; i >= 0; i--) {

			for (int _n = l.size(); _n >= 2 && ccw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {
				l.pop_back();
			}
			l.push_back(s[i]);
		}

		reverse(all(l));
		for (int i = u.size() - 2; i >= 1; i--)
		{
			l.push_back(u[i]);
		}

		return l;
	}
	void get_cin() {
		cin >> x >> y;
	}
};

class Segment {
public:
	Point p1, p2;
	Segment() {}
	Segment(Point p1, Point p2) :p1(p1), p2(p2) {}
	void get_cin() {
		cin >> p1.x >> p1.y >> p2.x >> p2.y;
	}
	Point p1tp2() {
		return p2 - p1;
	}
	Point p2tp1() {
		return p1 - p2;
	}
	double abs() {
		return std::abs(norm());
	}
	double norm() {
		return (p2 - p1).norm();
	}
};

bool Point::isOrthogonal(Segment s1, Segment s2) {
	return EQ(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool Point::isPalallel(Segment s1, Segment s2) {
	return EQ(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
bool Point::intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
Point Point::project(Segment s, Point p) {
	Point base = s.p2 - s.p1;
	double r = Point::dot(p - s.p1, base) / base.norm();
	return s.p1 + base * r;
}
Point Point::reflect(Segment s, Point p) {
	return (project(s, p) * 2) - p;
}
double Point::getDistanceLP(Segment s, Point p) {
	return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());
}
double Point::getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
	return getDistanceLP(s, p);
}
double Point::getDistance(Segment s1, Segment s2) {
	if (intersect(s1, s2)) return 0.0;
	return min({ getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)
		,getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2) });
}

Point Point::getIntersection(Segment s1, Segment s2) {
	// (s1.p1 - s2.p1).norm()
	auto bs = s1.p2 - s1.p1;
	auto n1 = s2.p1 - s1.p1;
	auto n2 = s2.p2 - s1.p1;
	auto c1 = std::abs(cross(n1, bs)) / bs.norm();
	auto c2 = std::abs(cross(n2, bs)) / bs.norm();
	return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));
	// c1:c2=t:1-t
	// c2t=(1-t)c1
	// t/(1-t)=c1/(c1+c2)
	// 
}

double arg(Point p) { return atan2(p.y, p.x); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
	void get_cin() {
		cin >> c.x >> c.y >> r;
	}
	static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
		double d = (c1.c - c2.c).abs(); // 中心点どうしの距離
		double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
		double t = arg(c2.c - c1.c);
		return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));

	}
};

pair<Point, Point> Point::crossPoints(Circle c, Segment s) {
	auto pp = project(s, c.c);
	auto f = (pp - c.c).norm();
	auto mu = sqrt(c.r * c.r - f);
	auto e = s.p1tp2() / s.p1tp2().abs();
	return make_pair(pp + e * mu, pp - e * mu);

}

ll divRm(string s, ll x) {

	ll r = 0;
	for (ll i = 0; i < s.size(); i++)
	{
		r *= 10;
		r += s[i] - '0';
		r %= x;
	}
	return r;
}
ll cmbi(ll x, ll b) {

	ll res = 1;
	for (size_t i = 0; i < b; i++)
	{
		res *= x - i;
		res %= INF;
		res *= inv[b - i];
		res %= INF;
	}
	return res;
}

double digsum(ll x) {
	ll res = 0;
	while (x > 0)
	{
		res += x % 10;
		x /= 10;
	}
	return res;
}
bool check_parindrome(string s) {
	int n = s.size();
	rep(i, n / 2) {
		if (s[i] != s[n - i - 1]) {
			return false;
		}

	}
	return true;
}

//　ここまでライブラリ
// ここからコード
void solv() {
	cin >> n;
	pll lr[100010];
	ll lmax = 0;
	ll rmin = INF;
	tuple3q<ll,ll,ll> q;
	pllgreaterq q2;
	rep(i, n) {
		cin >> lr[i].first >> lr[i].second;
		lmax = max(lr[i].first, lmax);
		rmin = min(lr[i].second, rmin);
		q2.psp2(lr[i].second, i);
		lr[i].second = -lr[i].second;
		q.push(make_tuple(lr[i].first, lr[i].second, i));
	}
	auto p = q.top();
	q.pop();
	auto p2 = q2.top();

	ll glm = get<0>(p);
	ll grm = -get<1>(p);
	ll i = get<2>(p);
	if (i == p2.second) {
		q2.pop();
	}
	rmin = q2.top().first;
	ll res = max(0LL, (rmin - lmax) + 1);
	res += grm - glm + 1;
	bool use[100010];
	all0(use);
	while (q.size() > 1)
	{
		p = q.top();
		q.pop();
		glm = max(glm, get<0>(p));
		grm = min(grm, -get<1>(p));
		i = get<2>(p);
		use[i] = true;
		while (!q2.empty())
		{
			if (use[q2.top().second]) {
				q2.pop();
			}
			else {
				break;
			}
		}
		p2 = q2.top();
		rmin = p2.first;

		res = max(res,
			max(0LL, grm - glm + 1) +
			max(0LL, rmin - lmax + 1));
	}

	cout << res << endl;

}


int main()
{
	//COMinit();
	solv();
	return 0;
}