C. Grid Xortime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputNote: 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.InputThe 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 FormatTo 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.OutputFor each test case, output a single integer — the XOR-sum of the whole grid.ExampleInput
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
Output
4
9
5
NoteFor the first test case, one possibility for Victor's original grid is:1324For the second test case, one possibility for Victor's original grid is:3885955155998429For the third test case, one possibility for Victor's original grid is:4321123456788991
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 
['constructive algorithms', 'greedy', 'implementation', 'interactive', 'math', '*2300']