Chef has a garden containing N cells. The i-th cell has R_{i} red flowers and B_{i} blue flowers. Chef can collect only one type of flowers (either red or blue) from each cell.

Let X denote the total number of red flowers Chef collects and Y denote the total number of blue flowers Chef collects. Chef wants to maximize the value of $\mathrm{min}(X, Y).$ Can you help Chef?

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

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N — the number of cells in Chef's garden.
• The second line of each test case contains $N space-separated integers R_{1}, R_{2}, \dots, R_{N}$ denoting the number of red flowers in each cell.
• The third line of each test case contains $N space-separated integers B_{1}, B_{2}, \dots, B_{N}$ denoting the number of blue flowers in each cell.

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

For each test case, output the maximum value of $\mathrm{min}(X, Y)$.

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

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 100$
$1 ≤ R_{i}, B_{i} ≤ 200$
- The sum of $N$ over all test cases does not exceed $100$.

----- Sample Input 1 ------
3
1
101
3
2
1 200
199 1
4
1 2 3 10
3 1 3 5

----- Sample Output 1 ------
0
199
7

----- explanation 1 ------
Test case 1:
If Chef collects $101$ red flowers from the cell, Chef will have a total of $101$ red flowers $(X = 101)$ and $0$ blue flowers $(Y = 0)$.
If Chef collects the $3$ blue flowers from the cell, Chef will have a total of $0$ red flowers $(X = 0)$ and $3$ blue flowers $(Y = 3)$.
Either way, $\mathrm{min}(X, Y) = 0$, the answer is $0$.

Test case 2: Chef collects the $199$ blue flowers from the first cell and the $200$ red flowers from the second cell, so $\mathrm{min}(X, Y) = 199$, which is maximum.

Test case 3: Chef collects blue cells from the first three cells $(Y = 3 + 1 + 3)$ and red flowers from the fourth cell $(X = 10)$, so $\mathrm{min}(X, Y) = 7$, which is maximum.

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