CF1617E.Christmas Chocolates

Christmas is coming, Icy has just received a box of chocolates from her grandparents! The box contains $n$ chocolates. The $i$-th chocolate has a non-negative integer type $a_i$.

Icy believes that good things come in pairs. Unfortunately, all types of chocolates are distinct (all $a_i$ are distinct). Icy wants to make at least one pair of chocolates the same type.

As a result, she asks her grandparents to perform some chocolate exchanges. Before performing any chocolate exchanges, Icy chooses two chocolates with indices $x$ and $y$ ($1 \le x, y \le n$, $x \ne y$).

In a chocolate exchange, Icy's grandparents choose a non-negative integer $k$, such that $2^k \ge a_x$, and change the type of the chocolate $x$ from $a_x$ to $2^k - a_x$ (that is, perform $a_x := 2^k - a_x$).

The chocolate exchanges will be stopped only when $a_x = a_y$. Note that other pairs of equal chocolate types do not stop the procedure.

Icy's grandparents are smart, so they would choose the sequence of chocolate exchanges that minimizes the number of exchanges needed. Since Icy likes causing trouble, she wants to maximize the minimum number of exchanges needed by choosing $x$ and $y$ appropriately. She wonders what is the optimal pair $(x, y)$ such that the minimum number of exchanges needed is maximized across all possible choices of $(x, y)$.

Since Icy is not good at math, she hopes that you can help her solve the problem.

圣诞节快到了，Icy 刚刚收到了祖父母送给她的一盒巧克力！盒子里共有 $n$ 块巧克力。第 $i$ 块巧克力的类型为一个非负整数 $a_i$。

Icy 相信好事成双。但不幸的是，所有巧克力的类型互不相同（即所有 $a_i$ 互异）。Icy 希望至少使一对巧克力的类型变得相同。

因此，她请祖父母进行若干次巧克力交换操作。在执行任何交换操作前，Icy 先选定两个下标 $x$ 和 $y$（满足 $1 \le x, y \le n$ 且 $x \ne y$）。

一次巧克力交换操作中，Icy 的祖父母选择一个非负整数 $k$，使得 $2^k \ge a_x$，并将第 $x$ 块巧克力的类型由 $a_x$ 改为 $2^k - a_x$（即执行赋值操作 $a_x := 2^k - a_x$）。

该交换过程仅在 $a_x = a_y$ 时停止。注意：其他任意一对相等的巧克力类型并不会导致过程停止。

Icy 的祖父母非常聪明，因此他们总会选择使所需交换次数最少的操作序列。而 Icy 喜欢制造麻烦，她希望通过对 $x$ 和 $y$ 的恰当选择，使得“最小所需交换次数”这一数值尽可能大。她想知道：在所有可能的 $(x, y)$ 对中，哪一对能使所需的最小交换次数达到最大值？

由于 Icy 不擅长数学，她希望你能帮她解决这个问题。

The first line of the input contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of chocolates.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$).

It is guaranteed that all $a_i$ are distinct.

输入的第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）—— 巧克力的数量。

输入的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 10^9$）。

保证所有 $a_i$ 互不相同。

Output three integers $x$, $y$, and $m$.

$x$ and $y$ are indices of the optimal chocolates to perform exchanges on. Your output must satisfy $1 \le x, y \le n$, $x \ne y$.

$m$ is the number of exchanges needed to obtain $a_x = a_y$. We can show that $m \le 10^9$ for any pair of chocolates.

If there are multiple solutions, output any.

输出三个整数 $x$、$y$ 和 $m$。

$x$ 和 $y$ 是执行交换操作的最优巧克力的下标。你的输出必须满足 $1 \le x, y \le n$ 且 $x \ne y$。

$m$ 是使 $a_x = a_y$ 所需的交换次数。可以证明：对于任意一对巧克力，均有 $m \le 10^9$。

若存在多个解，输出任意一个即可。

In the first test case, the minimum number of exchanges needed to exchange a chocolate of type $6$ to a chocolate of type $9$ is $5$. The sequence of exchanges is as follows: $6 \rightarrow 2 \rightarrow 0 \rightarrow 1 \rightarrow 7 \rightarrow 9$.

In the second test case, the minimum number of exchanges needed to exchange a chocolate of type $4$ to a chocolate of type $8$ is $2$. The sequence of exchanges is as follows: $4 \rightarrow 0 \rightarrow 8$.

在第一个测试用例中，将类型为 $6$ 的巧克力交换为类型为 $9$ 的巧克力所需的最少交换次数为 $5$。交换序列为：$6 \rightarrow 2 \rightarrow 0 \rightarrow 1 \rightarrow 7 \rightarrow 9$。

在第二个测试用例中，将类型为 $4$ 的巧克力交换为类型为 $8$ 的巧克力所需的最少交换次数为 $2$。交换序列为：$4 \rightarrow 0 \rightarrow 8$。