You have a total of 3N balls of colours Red, Blue and Green. There are exactly N balls of each colour.

These 3N balls are now distributed to 3 boxes such that each box contains exactly N balls. You are given the contents of each box.

You would like the 1^{st} box to contain all the red balls, the 2^{nd} box to contain all the green balls, and the 3^{rd} box to contain all the blue balls. Note that the given order of boxes is important here — it is not enough for each box to contain only balls of a single colour.

To achieve this, you can perform the following operation several (possibly, zero) times:
Pick any two distinct boxes, pick any one ball from each of these two boxes, and swap them.

Determine the minimum number of operations required to satisfy the given condition.

------ Input Format ------

• The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follows.
• Each test case consists of 4 lines of input.
• The first line of each test case contains a single integer N, denoting the number of balls of each colour.
• The i-th of the next three lines contains three space-separated integers R_{i}, G_{i} and B_{i} — the number of red, green, and blue balls in the i-th box respectively.

------ Output Format ------

For each test case, output a single line containing one integer — the minimum number of operations required such that the given condition is satisfied.

------ Constraints ------

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 1000$
$0 ≤ R_{i}, G_{i}, B_{i} ≤ N$
$R_{1} + G_{1} + B_{1} = R_{2} + G_{2} + B_{2} = R_{3} + G_{3} + B_{3} = N$
$R_{1} + R_{2} + R_{3} = G_{1} + G_{2} + G_{3} = B_{1} + B_{2} + B_{3} = N$

------ subtasks ------

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------
2
3
3 0 0
0 3 0
0 0 3
5
2 1 2
1 4 0
2 0 3
----- Sample Output 1 ------
0
3
----- explanation 1 ------
Test case $1$: Initially,
- The first box has $3$ red balls and none of any other colours
- The second box has $3$ green balls and none of any other colours
- The third box has $3$ blue balls and none of any other colours

The condition is already satisfied, and so no moves are required.

Test case $2$: One sequence of moves is as follows:
- Swap a green ball from the first box with a red ball from the second box.
- Swap a blue ball from the first box with a red ball from the third box.
- Once again, swap a blue ball from the first box with a red ball from the third box.

Now the first box has only red balls, the second has only green balls, and the third has only blue ones — as required.
It can be verified that no sequence of less than three moves achieves this result.

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