Description

When Miku cleans up the warehouse, She finds some boxes. All the boxes are cube, and the width of the i-th box is Ci=2^ki. Now, Miku prepares to throw these boxes away, but throwing them one by one is terrible, so she decides to put all boxes into a big box and throws it. Miku finds that only when box A's width is less than box B's, A can be put into B, and 8 boxes which width is 2^(k-1) can be put into 1 box which width is 2^k particular.

Now, please help Miku calculate how big of a box she needs to put all boxes into.

(If the biggest boxes of these boxes can meet the conditions, Miku will use this box, otherwise she will make a new box. Details please refer to the Sample Input.)

Input

The first line of input T is the number of test case.

There are three lines of each test case.

First, a integers n, means Miku find n different boxes.( 0 < n <= 50000)

Second, n intergers, k1, k2 ... kn, and ki means the i-th different box's width is 2^ki (0<=ki<=50000).

Third, n intergers, m1, m2 ... mn, and mi means the number of the i-th different box (1<=mi<=10000).

Output

For each test case output a interger K means the box's width is 2^K which Miku needs.

Sample Input

2
1
0
8
2
0 1
8 1

Sample Output

1
1

Hint

In test 1,Miku make a new box of 1 width.

In test 2,Miku use the 1 width's box her find in warehouse.

Author

qw4990