Consider a grid graph with $$$n$$$ rows and $$$n$$$ columns. Let the cell in row $$$x$$$ and column $$$y$$$ be $$$(x,y)$$$. There exists a directed edge from $$$(x,y)$$$ to $$$(x+1,y)$$$, with non-negative integer value $$$d_{x,y}$$$, for all $$$1\le x < n, 1\le y \le n$$$, and there also exists a directed edge from $$$(x,y)$$$ to $$$(x,y+1)$$$, with non-negative integer value $$$r_{x,y}$$$, for all $$$1\le x \le n, 1\le y < n$$$.

Initially, you are at $$$(1,1)$$$, with an empty set $$$S$$$. You need to walk along the edges and eventually reach $$$(n,n)$$$. Whenever you pass an edge, its value will be inserted into $$$S$$$. Please maximize the MEX$$$^{\text{∗}}$$$ of $$$S$$$ when you reach $$$(n,n)$$$.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\le t\le100$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\le n\le20$$$) — the number of rows and columns.

Each of the next $$$n-1$$$ lines contains $$$n$$$ integers separated by single spaces — the matrix $$$d$$$ ($$$0\le d_{x,y}\le 2n-2$$$).

Each of the next $$$n$$$ lines contains $$$n-1$$$ integers separated by single spaces — the matrix $$$r$$$ ($$$0\le r_{x,y}\le 2n-2$$$).

It is guaranteed that the sum of all $$$n^3$$$ does not exceed $$$8000$$$.
Output format:
For each test case, print a single integer — the maximum MEX of $$$S$$$ when you reach $$$(n,n)$$$.
Example Input 0:
2
3
1 0 2
0 1 3
2 1
0 3
3 0
3
1 2 0
0 1 2
2 0
1 2
0 1

Example Output 0:
3
2

Example Input 1:
1
10
16 7 3 15 9 17 1 15 9 0
4 3 1 12 13 10 10 14 6 12
3 1 3 9 5 16 0 12 7 12
11 4 8 7 13 7 15 13 9 2
2 3 9 9 4 12 17 7 10 15
10 6 15 17 13 6 15 9 4 9
13 3 3 14 1 2 10 10 12 16
8 2 9 13 18 7 1 6 2 6
15 12 2 6 0 0 13 3 7 17
7 3 17 17 10 15 12 14 15
4 3 3 17 3 13 11 16 6
16 17 7 7 12 5 2 4 10
18 9 9 3 5 9 1 16 7
1 0 4 2 10 10 12 2 1
4 14 15 16 15 5 8 4 18
7 18 10 11 2 0 14 8 18
2 17 6 0 9 6 13 5 11
5 15 7 11 6 3 17 14 5
1 3 16 16 13 1 0 13 11

Example Output 1:
14

Notes:
In the first test case, the grid graph and one of the optimal paths are as follows:

In the second test case, the grid graph and one of the optimal paths are as follows:

Example input:
2
3
1 0 2
0 1 3
2 1
0 3
3 0
3
1 2 0
0 1 2
2 0
1 2
0 1

1
10
16 7 3 15 9 17 1 15 9 0
4 3 1 12 13 10 10 14 6 12
3 1 3 9 5 16 0 12 7 12
11 4 8 7 13 7 15 13 9 2
2 3 9 9 4 12 17 7 10 15
10 6 15 17 13 6 15 9 4 9
13 3 3 14 1 2 10 10 12 16
8 2 9 13 18 7 1 6 2 6
15 12 2 6 0 0 13 3 7 17
7 3 17 17 10 15 12 14 15
4 3 3 17 3 13 11 16 6
16 17 7 7 12 5 2 4 10
18 9 9 3 5 9 1 16 7
1 0 4 2 10 10 12 2 1
4 14 15 16 15 5 8 4 18
7 18 10 11 2 0 14 8 18
2 17 6 0 9 6 13 5 11
5 15 7 11 6 3 17 14 5
1 3 16 16 13 1 0 13 11


Example output:
3
2

14