output_description: Print the maximum possible total joyfulness of the two contests.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      L_1 R_1
      L_2 R_2
      \vdots
      L_N R_N
attempt: import sys
  
  input = sys.stdin.readline
  
  ri = lambda: int(input())
  rs = lambda: input().rstrip()
  ril = lambda: list(map(int, input().split()))
  rsl = lambda: input().rstrip().split()
  ris = lambda n: [ri() for _ in range(n)]
  rss = lambda n: [rs() for _ in range(n)]
  rils = lambda n: [ril() for _ in range(n)]
  rsls = lambda n: [rsl() for _ in range(n)]
  
  n = ri()
  ls = rils(n)
  res = max(r - l + 1 for l, r in ls)
  
  ls.sort(key=lambda x: x[1])
  lmax0 = [ls[0][0]]
  rmin0 = [ls[0][1]]
  for i in range(1, n - 1):
      lmax0.append(max(lmax0[-1], ls[i][0]))
      rmin0.append(min(rmin0[-1], ls[i][1]))
  
  lmax1 = [ls[-1][0]]
  rmin1 = [ls[-1][1]]
  for i in range(1, n - 1):
      lmax1.append(max(lmax1[-1], ls[n - i - 1][0]))
      rmin1.append(min(rmin1[-1], ls[n - i - 1][1]))
  
  s0 = [max(0, r - l + 1) for l, r in zip(lmax0, rmin0)]
  s1 = [max(0, r - l + 1) for l, r in zip(lmax1, rmin1)]
  for x, y in zip(s0, reversed(s1)):
      res = max(res, x + y)
  
  ls.sort(key=lambda x: x[0])
  lmax0 = [ls[0][0]]
  rmin0 = [ls[0][1]]
  for i in range(1, n - 1):
      lmax0.append(max(lmax0[-1], ls[i][0]))
      rmin0.append(min(rmin0[-1], ls[i][1]))
  
  lmax1 = [ls[-1][0]]
  rmin1 = [ls[-1][1]]
  for i in range(1, n - 1):
      lmax1.append(max(lmax1[-1], ls[n - i - 1][0]))
      rmin1.append(min(rmin1[-1], ls[n - i - 1][1]))
  
  s0 = [max(0, r - l + 1) for l, r in zip(lmax0, rmin0)]
  s1 = [max(0, r - l + 1) for l, r in zip(lmax1, rmin1)]
  for x, y in zip(s0, reversed(s1)):
      res = max(res, x + y)
  
  ls.sort(key=lambda x: -x[1])
  lmax0 = [ls[0][0]]
  rmin0 = [ls[0][1]]
  for i in range(1, n - 1):
      lmax0.append(max(lmax0[-1], ls[i][0]))
      rmin0.append(min(rmin0[-1], ls[i][1]))
  
  lmax1 = [ls[-1][0]]
  rmin1 = [ls[-1][1]]
  for i in range(1, n - 1):
      lmax1.append(max(lmax1[-1], ls[n - i - 1][0]))
      rmin1.append(min(rmin1[-1], ls[n - i - 1][1]))
  
  s0 = [max(0, r - l + 1) for l, r in zip(lmax0, rmin0)]
  s1 = [max(0, r - l + 1) for l, r in zip(lmax1, rmin1)]
  for x, y in zip(s0, reversed(s1)):
      res = max(res, x + y)
  
  ls.sort(key=lambda x: -x[0])
  lmax0 = [ls[0][0]]
  rmin0 = [ls[0][1]]
  for i in range(1, n - 1):
      lmax0.append(max(lmax0[-1], ls[i][0]))
      rmin0.append(min(rmin0[-1], ls[i][1]))
  
  lmax1 = [ls[-1][0]]
  rmin1 = [ls[-1][1]]
  for i in range(1, n - 1):
      lmax1.append(max(lmax1[-1], ls[n - i - 1][0]))
      rmin1.append(min(rmin1[-1], ls[n - i - 1][1]))
  
  s0 = [max(0, r - l + 1) for l, r in zip(lmax0, rmin0)]
  s1 = [max(0, r - l + 1) for l, r in zip(lmax1, rmin1)]
  for x, y in zip(s0, reversed(s1)):
      res = max(res, x + y)
  
  print(res)
  
problem_description: 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.
samples: [{"input": "4\n    4 7\n    1 4\n    5 8\n    2 5", "output": "6\n    \n\nThe optimal choice is:\n\n  * 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.\n  * 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.\n  * The total joyfulness of these two contests is 6. We cannot make the total joyfulness greater than 6.\n\n* * *"}, {"input": "4\n    1 20\n    2 19\n    3 18\n    4 17", "output": "34\n    \n\n* * *"}, {"input": "10\n    457835016 996058008\n    456475528 529149798\n    455108441 512701454\n    455817105 523506955\n    457368248 814532746\n    455073228 459494089\n    456651538 774276744\n    457667152 974637457\n    457293701 800549465\n    456580262 636471526", "output": "540049931"}]