CF1361C.Johnny and Megan's Necklace

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 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!

约翰尼的妹妹梅根最近过生日了。哥哥送给她一个盒子，上面写着：“你美丽的项链——自己动手做！”。盒子里装着许多项链组件以及一些魔法胶水。

每个项链组件是一条连接两颗珍珠的链。每颗珍珠的颜色可用一个非负整数表示。魔法胶水允许梅根将两颗珍珠（可能来自同一项链组件）合并为一颗。颜色分别为 $u$ 和 $v$ 的两颗珍珠之间的连接的“美感”定义如下：设 $2^k$ 是能整除 $u \oplus v$ 的最大 2 的幂次（其中 $\oplus$ 表示 异或运算），则该连接的美感即为 $k$。若 $u = v$，则约定其美感为 $20$。

每颗珍珠最多只能与其他一颗珍珠合并一次。将两个项链组件中的珍珠合并，即可将这两个组件连接起来。通过多次使用胶水，梅根最终可构建出一条项链——它是由若干已连接的项链组件构成的一个环（即项链中每颗珍珠恰好与另一颗珍珠合并）。这样一条项链的美感定义为其中所有单个连接的美感的最小值。女孩希望用尽所有可用的项链组件，恰好构造出一条包含全部组件的项链，并使其美感尽可能大。请帮帮她！

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 $b$ $(0 \leq a, b \lt 2^{20})$, which denote colors of pearls presented in the necklace parts. Pearls in the $i$-th line have indices $2i - 1$ and $2i$ respectively.

第一行包含一个整数 $n$（$1 \leq n \leq 5 \cdot 10^5$），表示盒子中项链部件的数量。接下来的 $n$ 行中，每行包含两个整数 $a$ 和 $b$（$0 \leq a, b \lt 2^{20}$），分别表示该项链部件中两颗珍珠的颜色。第 $i$ 行中的珍珠对应编号分别为 $2i - 1$ 和 $2i$。

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.

第一行应包含一个整数 $b$，表示使用所有给定部件所能构造出的项链的最大可能美观度。

接下来的一行应包含 $2n$ 个互不相同的整数 $p_i$（$1 \leq p_i \leq 2n$）—— 表示初始珍珠的索引，按其在环状结构中出现的顺序排列。属于同一项链部件的珍珠索引在该排列中必须出现在相邻位置（因此 $1\,4\,3\,2$ 不是合法输出，而 $2\,1\,4\,3$ 和 $4\,3\,1\,2$ 是合法的）。若存在多种可能的答案，输出任意一种即可。

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.

在第一个例子中，以下珍珠对被连接：$(7, 9)$、$(10, 5)$、$(6, 1)$、$(2, 3)$ 和 $(4, 8)$。这些连接的美观度分别为：$3$、$3$、$3$、$20$、$20$。

下图展示了该构造。