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: def main():
      import sys
  
      input = sys.stdin.readline
  
      n = int(input())
      dg = 10**10
      lr = []
      for _ in [0] * n:
          lll, rrr = map(int, input().split())
          lr.append(lll * dg + rrr)
      lr.sort()
  
      # mirl[i],marl[i]:R0~Riのmin,max
      mirl = [10**10] * n
      marl = [0] * n
      for i, e in enumerate(lr):
          mirl[i] = min(mirl[i - 1], e % dg)
          marl[i] = max(marl[i - 1], e % dg)
  
      # mirr[i]:Ri~Rn-1のmin
      mirr = [0] * n
      mirr[-1] = lr[-1] % dg
      for i in range(n - 2, -1, -1):
          mirr[i] = min(mirr[i + 1], lr[i] % dg)
  
      L1 = lr[-1] // dg
      res = (lr[0] % dg - lr[0] // dg + 1) + max(0, mirr[1] - L1 + 1)
  
      for k in range(n - 2, 0, -1):
          # print(res)
          L2 = lr[k] // dg
          R1 = mirr[k + 1]
          R2 = lr[k] % dg
  
          restMaxR = marl[k - 1]
          restMinR = mirl[k - 1]
  
          # print(L1,L2,R1,R2,restMaxR,restMinR)
  
          tmp = max(0, min(restMaxR, R1) - L1 + 1) + max(0, min(restMinR, R2) - L2 + 1)
          tmp = max(
              tmp, max(0, min(restMinR, R1) - L1 + 1) + max(0, min(restMaxR, R2) - L2 + 1)
          )
          tmp = max(tmp, max(0, R1 - L1 + 1) + max(0, min(restMinR, R2) - L2 + 1))
          tmp = max(tmp, max(0, min(restMinR, R1) - L1 + 1), max(0, R2 - L2 + 1))
  
          res = max(res, tmp)
  
      print(res)
  
  
  if __name__ == "__main__":
      main()
  
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"}]