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 os
  import sys
  from io import BytesIO, IOBase
  
  from collections import defaultdict, Counter
  
  input = lambda: sys.stdin.readline().rstrip("\r\n")
  import math
  
  def I():
      return(int(input()))
  def lint():
      return(list(map(int,input().split())))
  def insr():
      s = input().strip()
      return(list(s[:len(s)]))
  def invr():
      return(map(int,input().split()))
  # Python program to print all
  # primes smaller than or equal to
  # n using Sieve of Eratosthenes
  
  import heapq
  
  def ask(a,b,c):
      print(f"? {a} {b} {c}")
      sys.stdout.flush()
      res=int(input())
      sys.stdout.flush()
      return res
  t=I()
  
  for _ in range(t):
      n = I()
      l = lint()
      m=max(l)
      arr = list(set(x % 3 for x in l))
      
      if m%3==0:
          if 1 in arr or 2 in arr:
              print(m//3+1)
          else:
              print(m//3)
      elif m%3==1:
          tmp=m//3
          if 2 in arr:
              tmp+=1
          if 1 in l or m-1 in l:
              tmp+=1
          
          print(max(m//3+1,tmp))
      else:
          if 1 in arr:
              
              print(m//3+2)
          else:
              
              print(m//3+1)
  
              
  
     
  
  
          
  
  
      