In CCPC contests, you will get "Time Limit Exceeded" when your program tried to run during too much time. Setting suitable time limit for problems is vital to a contest.
Mr. Bread is preparing problems for a coming contest with his friends. For each problem, there will be a "Main Correct Solution" denotes the standard solution program written by the author. There will also be several "Correct Solutions" denote solution programs intended to pass.
Assume there are $n$ programs in total, labeled by $1, 2, \\dots, n$. The $1$-th program denotes the "Main Correct Solution" while others are "Correct Solutions". The $i$-th program runs in $a_i$ seconds.
According to the rules in Mr. Bread's mind, the time limit $x$ should meet all the rules below:
Please write a program to find the time limit $x$.
The first line of the input contains an integer $T (1 <= T <= 10)$, denoting the number of test cases.
In each test case, there is one integer $n (2 <= n <= 10)$ in the first line, denoting the number of programs.
In the second line, there are $n$ integers $a_1, a_2,..., a_n (1 <= a_i <= 10)$.
For each test case, print a single line containing an integer, denoting the value of $x$.
## Input
The first line of the input contains an integer $T (1 <= T <= 10)$, denoting the number of test cases.In each test case, there is one integer $n (2 <= n <= 10)$ in the first line, denoting the number of programs.In the second line, there are $n$ integers $a_1, a_2,..., a_n (1 <= a_i <= 10)$.
## Output
For each test case, print a single line containing an integer, denoting the value of $x$.
[samples]
**Definitions**
Let $ P, Q \in \mathbb{R}^2 $ be two fixed pivot points.
Let $ A = \{A_1, A_2, \dots, A_n\} \subset \mathbb{R}^2 $ be a set of $ n $ distinct points, none lying on line $ \overleftrightarrow{PQ} $.
For any point $ A_i \in A $, define the **orientation** relative to triangle $ \triangle PQA_j $ as:
$ A_i $ is **inside** $ \triangle PQA_j $ (excluding boundary) if it lies in the interior of the triangle formed by $ P, Q, A_j $.
A **nested triangle sequence** is a strictly increasing sequence of indices $ v_1 < v_2 < \dots < v_k $ such that for all $ i \geq 2 $, point $ A_{v_i} $ lies strictly inside triangle $ \triangle P Q A_{v_{i-1}} $.
**Constraints**
1. $ 1 \leq T \leq 1000 $
2. For each test case:
- $ 1 \leq n \leq 10^5 $
- Coordinates of $ P, Q, A_i \in [-10^9, 10^9] $
- All points distinct; no $ A_i $ lies on line $ \overleftrightarrow{PQ} $
- Sum of $ n $ over all test cases $ \leq 10^6 $
**Objective**
Find the **maximum length** $ k $ of a nested triangle sequence $ v_1, v_2, \dots, v_k $, and among all such sequences of maximum length, return the **lexicographically smallest** one.
Lexicographic minimality: For two sequences $ \mathbf{v} = (v_1, \dots, v_k) $ and $ \mathbf{u} = (u_1, \dots, u_k) $, $ \mathbf{v} < \mathbf{u} $ iff there exists $ i \in \{1, \dots, k\} $ such that $ v_j = u_j $ for all $ j < i $ and $ v_i < u_i $.