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Problem - 2266A - Codeforces


A. Good Contest
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The next programming contest has three problems and $$$n$$$ participants.

Problem $$$1$$$ is easy, problem $$$2$$$ is medium, and problem $$$3$$$ is hard.

A participant is called weak if they did not solve all three problems.

Unfortunately, the scoreboard was lost. The only remaining information is an array $$$a$$$ of length $$$3$$$, where $$$a_i$$$ is the number of participants who solved problem $$$i$$$.

Among all scoreboards consistent with this information, find the minimum possible number of weak participants.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 3000$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 9$$$) — the number of participants.

The second line of each test case contains three integers $$$a_1, a_2, a_3$$$ ($$$0 \le a_i \le n$$$), where $$$a_i$$$ is the number of participants who solved problem $$$i$$$.

Output

For each test case, print a single integer — the minimum possible number of weak participants.

Example
Input
6
3
3 3 3
4
4 4 3
1
1 1 1
9
9 8 9
5
0 5 5
6
4 3 2
Output
0
1
0
1
5
4
Note

In the first test case, all $$$3$$$ participants can have solved all three problems, so the answer is $$$0$$$.

In the second test case, participant $$$1$$$ could have solved only problems $$$1$$$ and $$$2$$$, while participants $$$2$$$, $$$3$$$, and $$$4$$$ solved all three problems. Therefore, participant $$$1$$$ is the only participant who is weak, so the answer is $$$1$$$. It can be shown that this is minimal.