Description

Input

The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The next $2t$ lines contain descriptions of the test cases.

In the description of each test case, the first line contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the original length of the array $a$. The second line of the description lists $n$ space-separated integers $a_i$ ($-10^9 \leq a_i \leq 10^9$) — elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

Print $t$ lines, each of them containing the answer to the corresponding test case. The answer to the test case is a single integer — the maximal possible minimum in $a$, which can be obtained by several applications of the described operation to it.

8
1
10
2
0 0
3
-1 2 0
4
2 10 1 7
2
2 3
5
3 2 -4 -2 0
2
-1 1
1
-2

10
0
2
5
2
2
2
-2

Note

In the first example test case, the original length of the array $n = 1$. Therefore minimum extraction cannot be applied to it. Thus, the array remains unchanged and the answer is $a_1 = 10$.

In the second set of input data, the array will always consist only of zeros.

In the third set, the array will be changing as follows: $[\color{blue}{-1}, 2, 0] \to [3, \color{blue}{1}] \to [\color{blue}{2}]$. The minimum elements are highlighted with $\color{blue}{\text{blue}}$. The maximal one is $2$.

In the fourth set, the array will be modified as $[2, 10, \color{blue}{1}, 7] \to [\color{blue}{1}, 9, 6] \to [8, \color{blue}{5}] \to [\color{blue}{3}]$. Similarly, the maximum of the minimum elements is $5$.