CF1772D.Absolute Sorting

普及/提高-

通过率：0%

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题目描述

You are given an array $a$ consisting of $n$ integers. The array is sorted if $a_1 \le a_2 \le \dots \le a_n$ .

You want to make the array $a$ sorted by applying the following operation exactly once:

choose an integer $x$ , then for every $i \in [1, n]$ , replace $a_i$ by $|a_i - x|$ .

Find any value of $x$ that will make the array sorted, or report that there is no such value.

输入格式

The first line contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ). The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^8$ ).

Additional constraint on the input: the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

输出格式

For each test case, print any integer $x$ ( $0 \le x \le 10^9$ ) that makes the array sorted. It can be shown that if such an integer $x$ exists, there is at least one such integer between $0$ and $10^9$ .

If there is no such integer, then print $-1$ . If there are multiple suitable values of $x$ , print any of them.

输入输出样例

输入#1

8
5
5 3 3 3 5
4
5 3 4 5
8
1 2 3 4 5 6 7 8
6
10 5 4 3 2 1
3
3 3 1
3
42 43 42
2
100000000 99999999
6
29613295 52036613 75100585 78027446 81409090 73215

输出#1

说明/提示

In the first test case, after using $x = 4$ , the array becomes $[1, 1, 1, 1, 1]$ .

In the third test case, after using $x = 0$ , the array becomes $[1, 2, 3, 4, 5, 6, 7, 8]$ .

In the fourth test case, after using $x = 42$ , the array becomes $[32, 37, 38, 39, 40, 41]$ .

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