DIY Wooden Ladder

**PS:此翻译对原题意进行了修改。** 有$n$个数，依次为$a_1,a_2,a_3...a_n$。 然后你可以从中选出$k+2$个数（$k$为任意正整数）。 对于这$k+2$个数字，要满足第二大的数字至少比$k$大$1$。 问最大的符合条件的$k$为多少。 ## 输入格式 本题由$T$组数据构成（$1 \le T \le 100$） 每一组数据，第一行会给出$n$（$2 \le n \le 10^5$） 第二行有$n$个数字，第$i$个数字表示$a_i$（$1 \le a_i \le 10^5$） ## 输出格式 对于每一组数据，输出最大的符合条件的$k$。 ### 特别的，如果没有符合条件的$k$，则输出$0$。

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?

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 $ .

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.

4
4
1 3 1 3
3
3 3 2
5
2 3 3 4 2
3
1 1 2

2
1
2
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: