D. Exact Changetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne 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:   you have only coins of 1, 2 and 3 burles;  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?InputThe first line contains a single integer t (1 \le t \le 1000) — the number of test cases.The first line of each test case contains the single integer n (1 \le n \le 100) — the number of flavors in the store.The second line of each test case contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^9) — the cost of one bag of each flavor.OutputFor 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.ExampleInput
4
1
1337
3
10 8 10
5
1 2 3 4 5
3
7 77 777
Output
446
4
3
260
NoteIn 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 \cdot 3 + 1 \cdot 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 \cdot 3 + 1 \cdot 2 or 10 = 2 \cdot 3 + 2 \cdot 2.In the third test case, it's enough to take 1 coin of value 3 and 2 coins of value 1.
4
1
1337
3
10 8 10
5
1 2 3 4 5
3
7 77 777

446 4 3 260 
['brute force', 'constructive algorithms', 'greedy', '*2000']