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())
  p = []
  max_p = 1001001001
  max_i = 0
  max_len = 0
  for i in range(n):
      l, r = map(int, input().split())
      p.append([l, r])
      if max_p > l:
          max_p = l
          max_i = i
          max_len = r - l
      elif max_p == l:
          if r - l > max_len:
              max_i = i
              max_len = r - l
  min_p = 0
  min_i = 0
  for i in range(n):
      dif = min(p[max_i][0] - p[i][0], 0) + min(p[i][1] - p[max_i][1], 0)
      if dif < min_p:
          min_p = dif
          min_i = i
  g1 = []
  g2 = []
  max_l = p[max_i][0]
  max_r = p[max_i][1]
  min_l = p[min_i][0]
  min_r = p[min_i][1]
  g1.append(p[max_i])
  g2.append(p[min_i])
  for i in range(n):
      if i == max_i or i == min_i:
          continue
      if min(max_l - p[i][0], 0) + min(p[i][1] - max_r, 0) < min(
          min_l - p[i][0], 0
      ) + min(p[i][1] - min_r, 0):
          g2.append(p[i])
      else:
          g1.append(p[i])
  g1_l = 0
  g1_r = 1001001001
  g2_l = 0
  g2_r = 1001001001
  for i in range(len(g1)):
      if g1[i][0] > g1_l:
          g1_l = g1[i][0]
      if g1[i][1] < g1_r:
          g1_r = g1[i][1]
  for i in range(len(g2)):
      if g2[i][0] > g2_l:
          g2_l = g2[i][0]
      if g2[i][1] < g2_r:
          g2_r = g2[i][1]
  s_g1 = max(g1_r - g1_l + 1, 0)
  s_g2 = max(g2_r - g2_l + 1, 0)
  ans = s_g1 + s_g2
  print(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"}]