Grid Xor
Description
Note: The XOR-sum of set $\{s_1,s_2,\ldots,s_m\}$ is defined as $s_1 \oplus s_2 \oplus \ldots \oplus s_m$, where $\oplus$ denotes the bitwise XOR operation.
After almost winning IOI, Victor bought himself an $n\times n$ grid containing integers in each cell. $n$ is an even integer. The integer in the cell in the $i$-th row and $j$-th column is $a_{i,j}$.
Sadly, Mihai stole the grid from Victor and told him he would return it with only one condition: Victor has to tell Mihai the XOR-sum of all the integers in the whole grid.
Victor doesn't remember all the elements of the grid, but he remembers some information about it: For each cell, Victor remembers the XOR-sum of all its neighboring cells.
Two cells are considered neighbors if they share an edge — in other words, for some integers $1 \le i, j, k, l \le n$, the cell in the $i$-th row and $j$-th column is a neighbor of the cell in the $k$-th row and $l$-th column if $|i - k| = 1$ and $j = l$, or if $i = k$ and $|j - l| = 1$.
To get his grid back, Victor is asking you for your help. Can you use the information Victor remembers to find the XOR-sum of the whole grid?
It can be proven that the answer is unique.
The first line of the input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single even integer $n$ ($2 \leq n \leq 1000$) — the size of the grid.
Then follows $n$ lines, each containing $n$ integers. The $j$-th integer in the $i$-th of these lines represents the XOR-sum of the integers in all the neighbors of the cell in the $i$-th row and $j$-th column.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $1000$ and in the original grid $0 \leq a_{i, j} \leq 2^{30} - 1$.
Hack Format
To hack a solution, use the following format:
The first line should contain a single integer t ($1 \le t \le 100$) — the number of test cases.
The first line of each test case should contain a single even integer $n$ ($2 \leq n \leq 1000$) — the size of the grid.
Then $n$ lines should follow, each containing $n$ integers. The $j$-th integer in the $i$-th of these lines is $a_{i,j}$ in Victor's original grid. The values in the grid should be integers in the range $[0, 2^{30}-1]$
The sum of $n$ over all test cases must not exceed $1000$.
For each test case, output a single integer — the XOR-sum of the whole grid.
Input
The first line of the input contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single even integer $n$ ($2 \leq n \leq 1000$) — the size of the grid.
Then follows $n$ lines, each containing $n$ integers. The $j$-th integer in the $i$-th of these lines represents the XOR-sum of the integers in all the neighbors of the cell in the $i$-th row and $j$-th column.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $1000$ and in the original grid $0 \leq a_{i, j} \leq 2^{30} - 1$.
Hack Format
To hack a solution, use the following format:
The first line should contain a single integer t ($1 \le t \le 100$) — the number of test cases.
The first line of each test case should contain a single even integer $n$ ($2 \leq n \leq 1000$) — the size of the grid.
Then $n$ lines should follow, each containing $n$ integers. The $j$-th integer in the $i$-th of these lines is $a_{i,j}$ in Victor's original grid. The values in the grid should be integers in the range $[0, 2^{30}-1]$
The sum of $n$ over all test cases must not exceed $1000$.
Output
For each test case, output a single integer — the XOR-sum of the whole grid.
Samples
3
2
1 5
5 1
4
1 14 8 9
3 1 5 9
4 13 11 1
1 15 4 11
4
2 4 1 6
3 7 3 10
15 9 4 2
12 7 15 1
4
9
5
Note
For the first test case, one possibility for Victor's original grid is:
| $1$ | $3$ |
| $2$ | $4$ |
For the second test case, one possibility for Victor's original grid is:
| $3$ | $8$ | $8$ | $5$ |
| $9$ | $5$ | $5$ | $1$ |
| $5$ | $5$ | $9$ | $9$ |
| $8$ | $4$ | $2$ | $9$ |
For the third test case, one possibility for Victor's original grid is:
| $4$ | $3$ | $2$ | $1$ |
| $1$ | $2$ | $3$ | $4$ |
| $5$ | $6$ | $7$ | $8$ |
| $8$ | $9$ | $9$ | $1$ |