CF1197A.DIY Wooden Ladder

Let's denote a $k$-step ladder as the following structure: exactly $k + 2$ wooden planks, of which

• two planks of length at least $k+1$ — the base of the ladder;
• $k$ planks of length at least $1$ — the steps of the ladder;

Note that neither the base planks, nor the steps planks are required to be equal.

For example, ladders $1$ and $3$ are correct $2$-step ladders and ladder $2$ is a correct $1$-step ladder. On the first picture the lengths of planks are $[3, 3]$ for the base and $[1]$ for the step. On the second picture lengths are $[3, 3]$ for the base and $[2]$ for the step. On the third picture lengths are $[3, 4]$ for the base and $[2, 3]$ for the steps.

You have $n$ planks. The length of the $i$-th planks is $a_i$. You don't have a saw, so you can't cut the planks you have. Though you have a hammer and nails, so you can assemble the improvised "ladder" from the planks.

The question is: what is the maximum number $k$ such that you can choose some subset of the given planks and assemble a $k$-step ladder using them?

我们定义一个 $k$-级梯子为如下结构：恰好由 $k + 2$ 根木板组成，其中

• 两根长度至少为 $k+1$ 的木板——作为梯子的底边；
• $k$ 根长度至少为 $1$ 的木板——作为梯子的踏板；

注意：底边木板之间、踏板木板之间均不要求长度相等。

例如，图中梯子 $1$ 和 $3$ 是合法的 $2$-级梯子，而梯子 $2$ 是合法的 $1$-级梯子。第一幅图中，底边木板长度为 $[3, 3]$，踏板木板长度为 $[1]$；第二幅图中，底边木板长度为 $[3, 3]$，踏板木板长度为 $[2]$；第三幅图中，底边木板长度为 $[3, 4]$，踏板木板长度为 $[2, 3]$。

你有 $n$ 根木板，第 $i$ 根木板的长度为 $a_i$。你没有锯子，因此无法切割已有木板；但你有锤子和钉子，因此可以用这些木板组装一个临时的“梯子”。

问题是：你能从中选出若干木板并组装成一个 $k$-级梯子的最大 $k$ 值是多少？

The first line contains a single integer $T$ ($1 \le T \le 100$) — the number of queries. The queries are independent.

Each query consists of two lines. The first line contains a single integer $n$ ($2 \le n \le 10^5$) — the number of planks you have.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^5$) — the lengths of the corresponding planks.

It's guaranteed that the total number of planks from all queries doesn't exceed $10^5$.

第一行包含一个整数 $T$（$1 \le T \le 100$），表示查询次数。各次查询相互独立。

每次查询包含两行。第一行包含一个整数 $n$（$2 \le n \le 10^5$），表示你拥有的木板数量。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^5$），表示对应木板的长度。

保证所有查询中木板总数不超过 $10^5$。

Print $T$ integers — one per query. The $i$-th integer is the maximum number $k$, such that you can choose some subset of the planks given in the $i$-th query and assemble a $k$-step ladder using them.

Print $0$ if you can't make even $1$-step ladder from the given set of planks.

输出 $T$ 个整数——每个查询对应一个整数。其中第 $i$ 个整数表示最大的整数 $k$，使得你可以从第 $i$ 个查询所给的木板中选出某个子集，并用它们搭建一个 $k$ 级梯子。

若无法用给定的木板搭建出哪怕一个 $1$ 级梯子，则输出 $0$。

Examples for the queries $1-3$ are shown at the image in the legend section.

The Russian meme to express the quality of the ladders:

查询 $1$–$3$ 的示例见图注部分的图片。

表达梯子质量的俄罗斯网络迷因：