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.
1
1
6006

2002


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)

            

   


        


    