Increasing XOR

Task

An array $B$ consisting of $k$ positive integers is beautiful if and only if there exists an array $C = [C_0, C_1, \ldots, C_{k-1}]$ such that $C$ is a permutation of $B$ and the sequence of its prefix-XORs is strictly increasing. That is, $P_0 < P_1 < \dots < P_{k-1}$ where $P_i = C_0 \oplus C_1 \oplus \dots C_i$ for each $i = 0, \dots, k-1$.

The bitwise XOR $a \oplus b$ of two integers $a$ and $b$ is defined in the following way:
the $i$-th bit of $a \oplus b$ is $1$ if and only if exactly one among $a$ and $b$ has $1$ in the $i$-th bit.

Given an array $A$ consisting of $N$ positive integers, you have to determine for each non-empty prefix of $A$ whether it is beautiful.

Input data

The first line contains the only integer $N$. The second line contains $N$ integers, $A_0, A_1, \dots, A_{N-1}$.

Output data

You should print $N$ lines. In the $i$th line, you must write YES if the $i$th prefix is beautiful and NO otherwise.

Constraints and clarifications

• $1 \le N \le 200 \ 000$.
• $1 \le A_i < 2^{30}$ for each $i=0\ldots N-1$.

Example 1

stdin

5
3 1 4 1 5

stdout

YES
YES
YES
YES
NO

Explanation

In the first sample case:

• The $1$st prefix is beautiful because a sequence consisting of a single element is, by definition, strictly increasing.
• For the $2$nd prefix, the permutation $1, 3$ is suitable as the sequence $1, 2 = 1 \oplus 3$ is strictly increasing.
• For the $3$rd prefix, the permutation $1, 3, 4$ is suitable as the sequence $1, 2 = 1 \oplus 3, 6 = 1 \oplus 3 \oplus 4$ is strictly increasing.
• For the $4$th prefix, the permutation $1, 3, 4, 1$ is suitable as the sequence $1, 2, 6, 7$ is strictly increasing.
• It can be checked that the $5$th prefix is not beautiful.

Example 2

stdin

5
3 3 5 8 19

stdout

YES
NO
NO
NO
YES