Mocha and Math

题意翻译

给定一个长度为 $n$ 的数列 $a$，每次可以选择一个区间 $[l,r]$，对于 $0\le i\le r-l$，将 $a_{l+i}$ 变为 $a_{l+i}\ \operatorname{and}\ a_{r-i}$。其中 $\operatorname{and}$ 表示按位与。 你可以进行无限多次操作，问最终序列中最大值最小是多少。 译者 @_ajthreac_

题目描述

Mocha is a young girl from high school. She has learned so much interesting knowledge from her teachers, especially her math teacher. Recently, Mocha is learning about binary system and very interested in bitwise operation. This day, Mocha got a sequence $ a $ of length $ n $ . In each operation, she can select an arbitrary interval $ [l, r] $ and for all values $ i $ ( $ 0\leq i \leq r-l $ ), replace $ a_{l+i} $ with $ a_{l+i} \,\&\, a_{r-i} $ at the same time, where $ \& $ denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). This operation can be performed any number of times. For example, if $ n=5 $ , the array is $ [a_1,a_2,a_3,a_4,a_5] $ , and Mocha selects the interval $ [2,5] $ , then the new array is $ [a_1,a_2\,\&\, a_5, a_3\,\&\, a_4, a_4\,\&\, a_3, a_5\,\&\, a_2] $ . Now Mocha wants to minimize the maximum value in the sequence. As her best friend, can you help her to get the answer?

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Each test case consists of two lines. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 100 $ ) — the length of the sequence. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le 10^9 $ ).

输出格式

For each test case, print one integer — the minimal value of the maximum value in the sequence.

输入输出样例

输入样例 #1

4
2
1 2
3
1 1 3
4
3 11 3 7
5
11 7 15 3 7

输出样例 #1

0
1
3
3

说明

In the first test case, Mocha can choose the interval $ [1,2] $ , then the sequence becomes $ [ 0, 0] $ , where the first element is $ 1\,\&\,2 $ , and the second element is $ 2\,\&\,1 $ . In the second test case, Mocha can choose the interval $ [1,3] $ , then the sequence becomes $ [ 1,1,1] $ , where the first element is $ 1\,\&\,3 $ , the second element is $ 1\,\&\,1 $ , and the third element is $ 3\,\&\,1 $ .

题意翻译

给定一个长度为 $n$ 的数列 $a$，每次可以选择一个区间 $[l,r]$，对于 $0\le i\le r-l$，将 $a_{l+i}$ 变为 $a_{l+i}\ \operatorname{and}\ a_{r-i}$。其中 $\operatorname{and}$ 表示按位与。 你可以进行无限多次操作，问最终序列中最大值最小是多少。 译者 @_ajthreac_