Johnny and Megan's Necklace

题意翻译

$n$ 对珍珠由 $n$ 条线所连起来，共 $2n$ 颗。现在你可以在任意两个未被线连起来的珍珠之间连一条线，共可连 $n$ 条，使得这 $2n$ 颗珍珠形成一个环。设一条线所连的两颗珍珠权值为 $u,v$，则该线的权值为最大的整数 $k$ 满足 $2^k∣u \operatorname{xor} v$。如果 $u=v$，则 $k=20$。求所有新连的线的权值最小值的最大值并给出方案，即 $2n$ 颗珍珠所形成的的环。

题目描述

Johnny's younger sister Megan had a birthday recently. Her brother has bought her a box signed as "Your beautiful necklace — do it yourself!". It contains many necklace parts and some magic glue. The necklace part is a chain connecting two pearls. Color of each pearl can be defined by a non-negative integer. The magic glue allows Megan to merge two pearls (possibly from the same necklace part) into one. The beauty of a connection of pearls in colors $ u $ and $ v $ is defined as follows: let $ 2^k $ be the greatest power of two dividing $ u \oplus v $ — [exclusive or](https://en.wikipedia.org/wiki/Exclusive_or#Computer_science) of $ u $ and $ v $ . Then the beauty equals $ k $ . If $ u = v $ , you may assume that beauty is equal to $ 20 $ . Each pearl can be combined with another at most once. Merging two parts of a necklace connects them. Using the glue multiple times, Megan can finally build the necklace, which is a cycle made from connected necklace parts (so every pearl in the necklace is combined with precisely one other pearl in it). The beauty of such a necklace is the minimum beauty of a single connection in it. The girl wants to use all available necklace parts to build exactly one necklace consisting of all of them with the largest possible beauty. Help her!

输入输出格式

输入格式

The first line contains $ n $ $ (1 \leq n \leq 5 \cdot 10^5) $ — the number of necklace parts in the box. Each of the next $ n $ lines contains two integers $ a $ and $ b $ $ (0 \leq a, b < 2^{20}) $ , which denote colors of pearls presented in the necklace parts. Pearls in the $ i $ -th line have indices $ 2i - 1 $ and $ 2i $ respectively.

输出格式

The first line should contain a single integer $ b $ denoting the maximum possible beauty of a necklace built from all given parts. The following line should contain $ 2n $ distinct integers $ p_i $ $ (1 \leq p_i \leq 2n) $ — the indices of initial pearls in the order in which they appear on a cycle. Indices of pearls belonging to the same necklace part have to appear at neighboring positions in this permutation (so $ 1\,4\,3\,2 $ is not a valid output, whereas $ 2\,1\,4\,3 $ and $ 4\,3\,1\,2 $ are). If there are many possible answers, you can print any.

输入输出样例

输入样例 #1

5
13 11
11 1
3 5
17 1
9 27

输出样例 #1

3
8 7 9 10 5 6 1 2 3 4

输入样例 #2

5
13 11
11 1
3 5
17 1
7 29

输出样例 #2

2
8 7 10 9 5 6 4 3 2 1

输入样例 #3

1
1 1

输出样例 #3

20
2 1

说明

In the first example the following pairs of pearls are combined: $ (7, 9) $ , $ (10, 5) $ , $ (6, 1) $ , $ (2, 3) $ and $ (4, 8) $ . The beauties of connections equal correspondingly: $ 3 $ , $ 3 $ , $ 3 $ , $ 20 $ , $ 20 $ . The following drawing shows this construction.