Big Secret

2000ms

262144K

Description:

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.

Input:

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

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

Output:

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.

Sample Input:

3
1 2 3

Sample Output:

No

Sample Input:

6
4 7 7 12 31 61

Sample Output:

Yes
4 12 7 31 7 61

Note:

In the first example no permutation is valid.

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

Informação

Provedor Codeforces

Código CF925C