description: One day, early in the morning, you decided to buy yourself a bag of chips in the nearby store. The store has chips of n different flavors. A bag of the i-th flavor costs a_i burles.
  
  The store may run out of some flavors, so you'll decide which one to buy after arriving there. But there are two major flaws in this plan: 
  
    1. you have only coins of 1, 2 and 3 burles; 
    2. since it's morning, the store will ask you to pay in exact change, i. e. if you choose the i-th flavor, you'll have to pay exactly a_i burles. 
  
  
  
  Coins are heavy, so you'd like to take the least possible number of coins in total. That's why you are wondering: what is the minimum total number of coins you should take with you, so you can buy a bag of chips of any flavor in exact change?
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
  
  The first line of each test case contains the single integer n (1 ≤ n ≤ 100) — the number of flavors in the store.
  
  The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the cost of one bag of each flavor.
  
  Output
  
  For each test case, print one integer — the minimum number of coins you need to buy one bag of any flavor you'll choose in exact change.
  
  Example
  
  Input
  
  
  4
  1
  1337
  3
  10 8 10
  5
  1 2 3 4 5
  3
  7 77 777
  
  
  Output
  
  
  446
  4
  3
  260
  
  Note
  
  In the first test case, you should, for example, take with you 445 coins of value 3 and 1 coin of value 2. So, 1337 = 445 ⋅ 3 + 1 ⋅ 2.
  
  In the second test case, you should, for example, take 2 coins of value 3 and 2 coins of value 2. So you can pay either exactly 8 = 2 ⋅ 3 + 1 ⋅ 2 or 10 = 2 ⋅ 3 + 2 ⋅ 2.
  
  In the third test case, it's enough to take 1 coin of value 3 and 2 coins of value 1.
solution: import sys
  
  
  def exact_change(n, a):
      a.sort()
  
      _1 = 0
      _2 = 0
  
      for ai in a:
          r = ai % 3
          if r == 1:
              _1 = 1
          elif r == 2:
              _2 = 1
  
      r = a[-1] % 3
      if r == 0:
          if (_1 == 1) or (_2 == 1):
              return a[-1] // 3 + 1
          return a[-1] // 3
  
      if r == 2:
          if _1 == 0:
              return a[-1] // 3 + 1
          return a[-1] // 3 + 2
  
      if r == 1:
          if _2 == 0:
              return a[-1] // 3 + 1
          if a[0] == 1:
              return a[-1] // 3 + 2
  
          j = 2
          while j < n:
              if a[-1] - a[-j] == 1:
                  return a[-1] // 3 + 2
              if a[-1] - a[-j] > 1:
                  break
  
              j += 1
  
          return a[-1] // 3 + 1
  
  
  for _ in range(int(input())):
      n = int(input())
      a = list(map(int, input().split()))
      sys.stdout.write(f"{exact_change(n, a)}\n")
  