Non Zero Xor Codechef Solution

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Non Zero Xor Codechef Solution

Non Zero Xor Codechef Solution

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Problem

An array A of size N is called good if the following conditions hold:

  • For every pair (l, r) (1 \le l \le r \le N)A_l \oplus A_{l+1} \oplus … \oplus A_{r} \ne 0. (where \oplus denotes the bitwise XOR operation.)

JJ has an array A of size N. He wants to convert the array to a good array. To do so he can perform the following operation multiple times:

  • Pick an index i such that (1 \le i \le N) and set A_i := X where 0 \le X \lt 10^{10^{10}}.

Find the minimum number of operations required to convert A into a good array.

Input Format

  • The first line contains T – the number of test cases. Then the test cases follow.
  • The first line of each test case contains an integer N – the size of the array A.
  • The second line of each test case contains N space-separated integers A_1, A_2, \dots, A_N denoting the array A.

Output Format

For each test case, output the minimum number of operations required to convert the array A into a good array.

Constraints

  • 1 \leq T \leq 10^5
  • 1 \leq N \leq 10^5
  • 0 \leq A_i \lt 2^{30}
  • Sum of N over all test cases does not exceed 3 \cdot 10^5.

Sample 1:

Input

Output

3
5
1 2 3 4 4
3
0 0 0
6
2 3 5 7 11 13
2
3
0

Explanation:

Test Case 1: We can set A_2 = 4 and A_4 = 5. Thereby A will become [1, 4, 3, 5, 4] which is good. We can prove that we can not make A good in \lt 2 operations.

Test Case 2: We can set A_1 = 1A_2 = 10 and A_3 = 100. Thereby A will become [1, 10, 100] which is good. We can prove that we can not make A good in \lt 3 operations.

Test Case 3: The given array A is already good.

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SOLUTION

Non Zero Xor Codechef Solution

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