C. Big Secret
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence $$$a_1, \ldots, a_n$$$. In order to not reveal the secret earlier than needed, Vitya encrypted the answer and obtained the sequence $$$b_1, \ldots, b_n$$$ using the following rules:

  • $$$b_1 = a_1$$$;
  • $$$b_i = a_i \oplus a_{i - 1}$$$ for all $$$i$$$ from 2 to $$$n$$$, where $$$x \oplus y$$$ is the bitwise XOR of $$$x$$$ and $$$y$$$.

It is easy to see that the original sequence can be obtained using the rule $$$a_i = b_1 \oplus \ldots \oplus b_i$$$.

However, some time later Vitya discovered that the integers $$$b_i$$$ in the cypher got shuffled, and it can happen that when decrypted using the rule mentioned above, it can produce a sequence that is not increasing. In order to save his reputation in the scientific community, Vasya decided to find some permutation of integers $$$b_i$$$ so that the sequence $$$a_i = b_1 \oplus \ldots \oplus b_i$$$ is strictly increasing. Help him find such a permutation or determine that it is impossible.


The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$).

The second line contains $$$n$$$ integers $$$b_1, \ldots, b_n$$$ ($$$1 \leq b_i < 2^{60}$$$).


If there are no valid permutations, print a single line containing "No".

Otherwise in the first line print the word "Yes", and in the second line print integers $$$b'_1, \ldots, b'_n$$$ — a valid permutation of integers $$$b_i$$$. The unordered multisets $$$\{b_1, \ldots, b_n\}$$$ and $$$\{b'_1, \ldots, b'_n\}$$$ should be equal, i. e. for each integer $$$x$$$ the number of occurrences of $$$x$$$ in the first multiset should be equal to the number of occurrences of $$$x$$$ in the second multiset. Apart from this, the sequence $$$a_i = b'_1 \oplus \ldots \oplus b'_i$$$ should be strictly increasing.

If there are multiple answers, print any of them.

1 2 3
4 7 7 12 31 61
4 12 7 31 7 61

In the first example no permutation is valid.

In the second example the given answer lead to the sequence $$$a_1 = 4$$$, $$$a_2 = 8$$$, $$$a_3 = 15$$$, $$$a_4 = 16$$$, $$$a_5 = 23$$$, $$$a_6 = 42$$$.