## Xor Sort

Points: 100 (partial)
Time limit: 2.0s
Python 3 25.0s
Memory limit: 256M
Python 3 1G

Authors:
Problem types

It's been one year since the first arena contest! In a year we hosted many rated contests and we look forward to hosting more frequent contests in the future.

After each rated contest, participants' ratings change. Your tasks is to write a new rating algorithm.

You will be given an array $$a$$ of $$n$$ integers, where $$a_i$$ represents the rating of the $$ith$$ contestant, from the bottom of the standing (contestant $$1$$ was the last one). Your objective is to make this array sorted in non-decreasing order by doing the following operation :

For each $$i$$ starting from the beginning of the array ($$i = 1$$) to the end ($$i = n$$) you can choose one index $$j > i$$ and replace $$a_i$$ with $$a_i$$ $$xor$$ $$a_j$$, or you can skip this index $$i$$ and not perform any operation at all.

Elements should be modified in the same order they appear in the array, that is, element $$a_p$$ cannot be modified if any element $$a_q, q > p$$ was already modified.

#### Input Specification

The first line of the input contains one integer $$t$$ ($$1\leq t \leq 10^4$$) - the number of test cases. Then $$t$$ test cases follow.

Each test case contains two lines. The first line of each test case contains one integer $$n$$ ($$1 \leq n \leq 10^5$$) - the number of elements in the array.

The second line of the test case contains $$n$$ integers $$a_1,a_2,...,a_n$$ ($$0 \leq a_i \leq 10^9$$).

It is guaranteed that the sum of n over all test cases does not exceed $$10^5$$.

#### Output Specification

For each test case, in a new line output "YES" if it is possible to sort the array in non descending order otherwise print "NO"

#### Scoring

• (6 points) $$1 \leq n \leq 10^5$$ and $$a_i \leq 32$$

• (6 points) $$1 \leq n \leq 10^5$$ and $$a_i$$ is a power of $$2$$

• (10 points) sum of $$n$$ over all test cases does not exceed $$2000$$

• (18 points) no additional constraints

#### Sample Input

3
5
17 16 0 16 16
5
2 27 30 16 16
4
7 7 7 1

#### Sample Output

YES
YES
NO