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: N = int(input())
  LR = [list(map(int, input().split())) for _ in range(N)]
  
  
  def myeval(arg):
      if arg[0] != None:
          L_tmp, R_tmp = arg[0]
          score = max(0, R_tmp - L_tmp + 1)
      else:
          score = 0
      if arg[1] != None:
          L_tmp, R_tmp = arg[1]
          score += max(0, R_tmp - L_tmp + 1)
      else:
          score += 0
      return score
  
  
  ans = [None, None]
  for i, (Li, Ri) in enumerate(LR):
      # print("#", ans, myeval(ans))
      # add left
      ans_l = list(ans)
      if ans_l[0] != None:
          L_tmp, R_tmp = ans_l[0]
      else:
          L_tmp, R_tmp = (0, 10**9 + 7)
      ans_l[0] = (max(L_tmp, Li), min(R_tmp, Ri))
      # add right
      ans_r = list(ans)
      if ans_r[1] != None:
          L_tmp, R_tmp = ans_r[1]
      else:
          L_tmp, R_tmp = (0, 10**9 + 7)
      ans_r[1] = (max(L_tmp, Li), min(R_tmp, Ri))
      # evaluate score
      score_l = myeval(ans_l)
      score_r = myeval(ans_r)
      # judge
      if score_l < score_r:
          ans = list(ans_r)
      else:
          ans = list(ans_l)
  
  print(myeval(ans))
  
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"}]