E. Constructive Xor
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a sequence of $$$n$$$ integers $$$a_1, a_2, \dots , a_n$$$ .

Your task is to answer $$$q$$$ queries:

- Choose several numbers from $$$a_1, a_2, \dots , a_n$$$ such that their bitwise XOR is $$$x$$$. If their are multiple solutions, print any of them.

It's guaranteed that at least one solution exists for each query.

Input

The first line of input contains a single integer $$$n \ (1 \le n \le 500)$$$.

The second line contains $$$n$$$ integers $$$a_1, \dots, a_n \ (0 \le a_i \lt 2^{60})$$$.

Then, the third line contains a single integer $$$q \ (1 \le q \le 1000)$$$.

For the next $$$q$$$ lines, each line contains a single integer $$$x \ (0 \le x \lt 2^{60})$$$ denoting a query.

Output

For each query, print a line of $$$n$$$ zeros and/or ones. The $$$i$$$-th character should be '1' if the solution contains $$$a_i$$$, or should be '0' otherwise.

Example
Input
6
2 15 12 0 5 4
5
10
8
3
6
7
Output
010010
110010
011000
011010
100010