Bob was experimenting with an array of numbers in an effort to make a programming problem, finally he made an interesting problem but he cannot solve it, can you help Bob?
Given an array A of n integers, Bob wants you to answer q different queries based on the given array. For each query Bob wants to know the minimum number of values he should remove from the array A to make the XOR of the remaining values in the array equal to x.
NOTE: The XOR of an empty array is 0.
Reference: Bitwise XOR
INPUT FORMAT
The first line of the input contains an integer n (1<=n<=105) - the number of values in the array.
The second line of the input contains n integers a1,a2,a3,..an (1<=ai<=200) - the values in the array.
The third line of the input contains an integer q (1<=n<=105) - the number of queries.
Each of the next q lines contains one integer xi (0<=xi<=200) - the queried value.
OUTPUT FORMAT
Print q integers. The ith integer should represent the minimum number of values to remove from A to make the XOR equal to xi, or −1 if it is impossible.
In the sample input, A=[13,17,2,50,55] and there are 4 queries:
For the first query x=46, removing 2 & 55 from A gives you an array [13,17,50] with a total XOR of 46. Hence, the answer for the first query is 2. It can be shown that you can't make the XOR equal to 46 with less than 2 removals.
Likewise, For the second query x=22, removing 13 from A gives you an array [17,2,50,55] with a total XOR of 22. The answer to this query is 1.
For the third query, removing all the 5 values in the array gives an array with XOR as 0, and it is the optimal solution.
In the fourth and final query, it is not possible to remove values to make the XOR of the array equal to 200, so the answer is −1.
