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)

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif
#define y0 qvya13579
#define y1 qvyb24680
#define j0 qvja13579
#define j1 qvjb24680
#define next qvne13579xt
#define prev qvpr13579ev
#define INF 1000000007
#define MOD 1000000007
#define endl "\n"
#define PI acos(-1.0)
#define IOS cin.tie(0);ios::sync_with_stdio(false)
#if __cplusplus < 201103L
#define stoi(argument_string) atoi((argument_string).c_str())
#define stoll(argument_string) atoll((argument_string).c_str())
#endif
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define REP_R(i,n) for(int i=((int)(n)-1);i>=0;--i)
#define FOR(i,m,n) for(int i=((int)(m));i<(int)(n);++i)
#define FOR_R(i,m,n) for(int i=((int)(m)-1);i>=(int)(n);--i)
#define ALL(v) (v).begin(),(v).end()
#define RALL(v) (v).rbegin(),(v).rend()
#define SIZ(x) ((int)(x).size())
#define CIN(x) cin>>(x)
#define CIN2(x,y) cin>>(x)>>(y)
#define CIN3(x,y,z) cin>>(x)>>(y)>>(z)
#define CIN4(x,y,z,w) cin>>(x)>>(y)>>(z)>>(w)
#define CIN5(x,y,z,w,u) cin>>(x)>>(y)>>(z)>>(w)>>(u)
#define SCAND(x) scanf("%d",&(x))
#define SCAND2(x,y) scanf("%d%d",&(x),&(y))
#define SCAND3(x,y,z) scanf("%d%d%d",&(x),&(y),&(z))
#define SCAND4(x,y,z,w) scanf("%d%d%d%d",&(x),&(y),&(z),&(w))
#define SCAND5(x,y,z,w,u) scanf("%d%d%d%d%d",&(x),&(y),&(z),&(w),&(u))
#define SCANLLD(x) scanf("%lld",&(x))
#define SCANLLD2(x,y) scanf("%lld%lld",&(x),&(y))
#define SCANLLD3(x,y,z) scanf("%lld%lld%lld",&(x),&(y),&(z))
#define SCANLLD4(x,y,z,w) scanf("%lld%lld%lld%lld",&(x),&(y),&(z),&(w))
#define SCANLLD5(x,y,z,w,u) scanf("%lld%lld%lld%lld%lld",&(x),&(y),&(z),&(w),&(u))
#define I64DSCAN(x) scanf("%I64d",&(x))
#define I64DSCAN2(x,y) scanf("%I64d%I64d",&(x),&(y))
#define I64DSCAN3(x,y,z) scanf("%I64d%I64d%I64d",&(x),&(y),&(z))
#define I64DSCAN4(x,y,z,w) scanf("%I64d%I64d%I64d%I64d",&(x),&(y),&(z),&(w))
#define I64DSCAN5(x,y,z,w,u) scanf("%I64d%I64d%I64d%I64d%I64d",&(x),&(y),&(z),&(w),&(u))
#define PRINTD(x) printf("%d\n",(x))
#define PRINTLLD(x) printf("%lld\n",(x))
#define PRINTI64D(x) printf("%I64d\n",(x))
#define DEBUG(argument) cerr<<(#argument)<<" : "<<(argument)<<"\n"
typedef long long lli;
typedef unsigned long long ulli;
using namespace std;


int ctoi(char c)
{
  if( c >= '0' and c <= '9' )
    {
      return (int)(c-'0');
    }

  return -1;
}

int alphabet_pos(char c) 
{
  if( c >= 'a' and c <= 'z' )
    {
      return (int)(c-'a');
    }

  return -1;
}


int alphabet_pos_capital(char c)
{
  if( c >= 'A' and c <= 'Z' )
    {
      return (int)(c-'A');
    }

  return -1;
}


vector<string> split(string str, char ch)
{
  int first = 0;
  int last = str.find_first_of(ch);
  
  if(last == string::npos)
    {
      last = SIZ(str);
    }

  vector<string> result;

  while( first < SIZ(str) )
    {
      string Ssubstr(str, first, last - first);
      result.push_back(Ssubstr);
      first = last + 1;
      last = str.find_first_of(ch, first);

      if(last == string::npos)
	{
	  last = SIZ(str);
	}
    }
  
  return result;
}



int gcd( int a , int b ) // assuming a,b >= 1
{
  if( a < b )
    {
      swap(a,b);
    }

  if( b == 0 )
    {
      return a;
    }
  
  if( a % b == 0 )
    {
      return b;    
    }

  return gcd( b , a % b );
  
}

long long gcd( long long a , long long b ) // assuming a,b >= 1
{
  if( a < b )
    {
      swap(a,b);
    }

  if( b == 0LL )
    {
      return a;
    }
  
  if( a % b == 0 )
    {
      return b;
    }

  return gcd( b , a % b );
  
}

int lcm( int a , int b ) // assuming a,b >= 1
{
  return  a * b / gcd( a , b );
  
}

long long lcm( long long a , long long b ) // assuming a,b >= 1
{
  return  a * b / gcd( a , b );
  
}

long long pow_fast( long long x, long long n_power , long long modulus )
{
  
  if( n_power == 0 )
    {
      return 1;
    }
  
  if( n_power % 2 == 0)
    {
      return pow_fast( x * x % modulus , n_power / 2 , modulus );  
    }

  
  return x * pow_fast( x , n_power - 1 , modulus ) % modulus;
}


struct CombinationTable
{
  vector<vector<long long> > val;

  CombinationTable( int size ) : val( size+1 , vector<long long>( size+1 ) ) //constructor
  {
    for( int i = 0 ; i <= size ; ++ i ) // note that 0 <= i <= size
      {

	for( int j = 0 ; j <= i ; ++ j )
	  {
	    
	    if( j == 0 or j == i )
	      {
		val[i][j] = 1LL;
	      }
	    else
	      {
		val[i][j] = val[i-1][j-1] + val[i-1][j];
	      }

	  }
	
	
      }
    
  }

  
};


void print_vector(vector<int> h,bool verbose = true)
{
  int L =  h.size();
  
  for(int i = 0; i < L; ++ i)
    {
      if( verbose )
	{
	  printf("%d",h[i]);
	}
      else
	{
	  cerr << h[i];
	}

      if( i != L-1 )
	{
	  if( verbose )
	    {
	      printf(" ");
	    }
	  else
	    {
	      cerr << " ";
	    }
	}
      else
	{
	  if( verbose )
	    {
	      printf("\n");
	    }
	  else
	    {
	      cerr << "\n";
	    }
	}
    }    
}

void print_vector(vector<long long> h,bool verbose = true)
{
  int L =  h.size();
  
  for(int i = 0; i < L; ++ i)
    {
      if( verbose )
	{
	  printf("%lld",h[i]);
	}
      else
	{
	  cerr << h[i];
	}

      if( i != L-1 )
	{
	  if( verbose )
	    {
	      printf(" ");
	    }
	  else
	    {
	      cerr << " ";
	    }
	}
      else
	{
	  if( verbose )
	    {
	      printf("\n");
	    }
	  else
	    {
	      cerr << "\n";
	    }
	}
    }    
}



void print_matrix2D(vector<vector<int> > h, bool verbose = true)
{
  int Ly =  h.size();
        
  for(int i = 0; i < Ly; ++ i)
    {
      int Lx = h[i].size(); 
      for(int j = 0; j < Lx; ++ j)
        {	  
	  if( verbose )
	    {
	      printf("%d",h[i][j]);
	    }
	  else
	    {
	      cerr << h[i][j];
	    }
	  
	  if( j != Lx-1 )
	    {
	      if( verbose )
		{
		  printf(" ");
		}
	      else
		{
		  cerr << " ";
		}
	    }
	  else
	    {
	      if( verbose )
		{
		  printf("\n");
		}
	      else
		{
		  cerr << "\n";
		}
	    }	  
        }
    }    
}

void print_matrix2D(vector<vector<long long> > h, bool verbose = true)
{
  int Ly =  h.size();
        
  for(int i = 0; i < Ly; ++ i)
    {
      int Lx = h[i].size();
      for(int j = 0; j < Lx; ++ j)
        {
	  if( verbose )
	    {
	      printf("%lld",h[i][j]);
	    }
	  else
	    {
	      cerr << h[i][j];
	    }

	  if( j != Lx-1 )
	    {
	      if( verbose )
		{
		  printf(" ");
		}
	      else
		{
		  cerr << " ";
		}
	    }
	  else
	    {
	      if( verbose )
		{
		  printf("\n");
		}
	      else
		{
		  cerr << "\n";
		}
	    }
        }
    }
}

void print_matrix2D(vector<string> h, bool verbose = true)
{
  int Ly =  h.size();
        
  for(int i = 0; i < Ly; ++ i)
    {
      int Lx = h[i].size();
      for(int j = 0; j < Lx; ++ j)
        {
	  if( verbose )
	    {
	      printf("%c",h[i][j]);
	    }
	  else
	    {
	      cerr << h[i][j];
	    }
        }
      
      if( verbose )
	{
	  printf("\n");
	}
      else
	{
	  cerr << "\n";
	}
    }    
}

void print_binary(int val, int num_digit = 31, bool verbose = false)
{
  for(int k = num_digit-1; k >= 0; -- k)
    {
      if( verbose )
	{
	  printf("%d",(val>>k)&1);
	}
      else
	{
	  cerr << ((val>>k)&1);
	}    
    }
  
  if( verbose )
    {
      printf("\n");
    }
  else
    {
      cerr << "\n";
    }
}

void print_binary(long long val, int num_digit = 63, bool verbose = false)
{
  for(int k = num_digit-1; k >= 0; -- k)
    {
      if( verbose )
	{
	  printf("%lld",((val>>k)&1));
	}
      else
	{
	  cerr << ((val>>k)&1);
	}    
    }
  
  if( verbose )
    {
      printf("\n");
    }
  else
    {
      cerr << "\n";
    }
}



struct UnionFind //size-based
{
  vector<int> parent, treesize;
  
  UnionFind( int size ) : parent( size ) , treesize( size , 1 ) //constructor
  {
    for( int i = 0 ; i < size ; ++ i )
      {
	parent[i] = i;
      }
  }

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

  void unite( int x, int y )
  {
    x = root(x); 
    y = root(y);
    
    if( x == y )
      {
	return; 
      }

    if( treesize[x] < treesize[y] )
      {
	parent[x] = y;
	treesize[y] += treesize[x];
      }
    else
      {
	parent[y] = x;
	treesize[x] += treesize[y];	
      }
    
  }

  bool sametree( int x, int y )
  {
    return root(x) == root(y);
  }

  int gettreesize( int x )
  {
    return treesize[root(x)];
  }
  
};

template< typename Type_value >
struct SegmentTree //Range Minimum Query (RMQ)
{

private:
  int n;
  vector<Type_value> node;
  Type_value identity_element_segmenttree;
  
public:
  SegmentTree( vector<Type_value> v, Type_value identity_element_st ) //constructor
  {
    int sz = v.size();
    identity_element_segmenttree = identity_element_st;
    n = 1;
    while(n < sz)
      {
	n <<= 1;
      }
    
    node.resize(2*n-1, identity_element_segmenttree);

    for( int i = 0 ; i < sz ; ++ i )
      {
	node[i+n-1] = v[i];
      }
    
    for( int i = n-2 ; i >= 0 ; -- i )
      {
	node[i] = min(node[2*i+1], node[2*i+2]);
      } 
  }
 
  void update(int x, Type_value val)
  {
    x += (n - 1);
    node[x] = val;
    
    while( x > 0 )
      {
	x = (x - 1) / 2;
	node[x] = min(node[2*x+1], node[2*x+2]);
      }
  }
 
  Type_value getmin( int a, int b, int k = 0, int l = 0, int r = -1 ) //getting minimum value in [a,b)
  {
    // k : index of the referred node
    // [l,r) : range covered by the k-th node 
    
    if( r < 0 )
      {
	r = n;
      } 
    if( r <= a or b <= l )
      {
	return identity_element_segmenttree;
      } 
    if( a <= l and r <= b )
      {
	return node[k];
      }
    
    Type_value vl = getmin(a, b, 2*k+1, l, (l+r)/2);
    Type_value vr = getmin(a, b, 2*k+2, (l+r)/2, r);
    return min(vl, vr);
  }
  
};


template< typename Type_value >
struct BinaryIndexedTree //Range Sum Query (RSQ), 0-indexed
{
  
private:
  int size_;
  vector< Type_value > data;

public:
  BinaryIndexedTree(int sz, Type_value identity_element_binaryindexedtree = 0.0 ) // constructor
  {
    size_ = sz;
    data.resize(sz+1,identity_element_binaryindexedtree);
  }

  Type_value sum(int i) //sum within [0,i)
  {
    if( i <= 0 )
      {
	return (Type_value) 0.0;
      }

    if( i > size_ )
      {
	i = size_;
      }
    
    Type_value sm = 0.0;
    while( i > 0 )
      {
	sm += data[i];
	i -= i & -i;
      }
    
    return sm;
  }

  void add(int i, Type_value x)
  {
    if( i < 0 or i >= size_ )
      {
	return;
      }
    ++ i;
    while( i <= size_ )
      {
	data[i] += x;
	i += i & -i;
      }
  }
};

struct RollingHash
{

  /*
    10 primes near 1e9(for other mod(s)):
    {
    1000000007,
    1000000009,
    1000000021,
    1000000033,
    1000000087,
    1000000093,
    1000000097,
    1000000103,
    1000000123,
    1000000181
    }

    10 primes near 1e5(for other base(s)):
    {100003,
    100019,
    100043,
    100049,
    100057,
    100069,
    100103,
    100109,
    100129,
    100151}
  */
  
private:
  vector<unsigned long long> hash;
  vector<unsigned long long> base_pow;
  unsigned long long base, modulus;

  const unsigned long long MODULUS_DEFAULT = (1ULL << 61) - 1;
  const unsigned long long MASK30 = (1ULL << 30) - 1;
  const unsigned long long MASK31 = (1ULL << 31) - 1;
  const unsigned long long BASE_MIN = 1e7;

  unsigned long long Modulus_2pow61m1( unsigned long long val )
  {
    val = (val & MODULUS_DEFAULT) + (val >> 61);

    if( MODULUS_DEFAULT < val )
      {
	val -= MODULUS_DEFAULT;
      }

    return val;
  }
  

  unsigned long long Multiple_2pow61m1( unsigned long long a, unsigned long long b )
  {
    unsigned long long au = a >> 31;
    unsigned long long ad = a & MASK31;
    unsigned long long bu = b >> 31;
    unsigned long long bd = b & MASK31;

    unsigned long long mid = ad * bu + au * bd;
    unsigned long long midu = mid >> 30;
    unsigned long long midd = mid & MASK30;

    return Modulus_2pow61m1( ( (au * bu) << 1 ) + midu + (midd << 31) + ad * bd );
  }
 
  void initialize(string& S)
  {
    int N = S.size();
    vector<int> s(N);
    for(int i = 0; i < N; ++i)
      {
	s[i] = S[i];
      }
    
    initialize(s);
  }
 
  void initialize(vector<int>& S)
  {
    hash.resize(S.size()+1);
    base_pow.resize(S.size()+1);
    hash[0] = 0;
    base_pow[0] = 1;

    if( modulus == MODULUS_DEFAULT )
      {	
	for(int i = 1; i <= S.size(); ++i)
	  {
	    hash[i] = Modulus_2pow61m1( Multiple_2pow61m1(hash[i-1],base) + S[i-1] );
	    base_pow[i] = Multiple_2pow61m1(base_pow[i-1],base);
	  }
      }
    else
      {
	for(int i = 1; i <= S.size(); ++i)
	  {
	    hash[i] = ( hash[i-1] * base + S[i-1] ) % modulus;
	    base_pow[i] = ( base_pow[i-1] * base ) % modulus;
	  }
      }
  }

public:
  RollingHash(string S = "", unsigned long long base_ = 0, unsigned long long modulus_ = 0)
  {
    if( 0 < modulus_ )
      {
	modulus = modulus_;
      }
    else
      {
	modulus = MODULUS_DEFAULT;
      }

    if( 0 < base_ )
      {
	base = base_;
      }
    else
      {
	mt19937_64 mt64(static_cast<unsigned int>(time(nullptr)));
	uniform_int_distribution<unsigned long long> rand_uniform(BASE_MIN,modulus-BASE_MIN);
	base = rand_uniform(mt64);
      }

    if( S.size() > 0 )
      {
	initialize(S);
      }
  }
  
  // 0-indexed, [a, b)
  unsigned long long between(int a, int b)
  {
    if( modulus == MODULUS_DEFAULT )
      {
	return Modulus_2pow61m1( modulus + hash[b] - Multiple_2pow61m1(hash[a],base_pow[b-a]) );
      }
    
    return ( modulus + hash[b] - ( hash[a] * base_pow[b-a] ) % modulus ) % modulus;
  }
};


/*------------------ the end of the template -----------------------*/









signed main()
{
  IOS; /* making cin faster */
  const int M = 1e9;
  int N;
  SCAND(N);
  vector<pair<lli,lli> > P(N);
  REP(i,N)
    {
      SCANLLD2(P[i].first,P[i].second);
    }
  sort(ALL(P),[](pair<lli,lli> a, pair<lli,lli> b)
       {
	 return a.second - a.first < b.second - b.first;
       });
  
  vector<lli> numl(N);
  lli rl = 1;
  lli rr = M;

  REP(i,N)
    {
      rl = max(rl,P[i].first);
      rr = min(rr,P[i].second);

      numl[i] = max(rr-rl+1,0LL);
    }

  vector<lli> numr(N);
  rl = 1;
  rr = M;

  REP_R(i,N)
    {
      rl = max(rl,P[i].first);
      rr = min(rr,P[i].second);

      numr[i] = max(rr-rl+1,0LL);
    }

  lli ans = 0;
  REP(i,N-1)
    {
      ans = max(ans,numl[i]+numr[i+1]);
    }

  PRINTLLD(ans);
  
  

  

}