CF2263A.Min Max Game

Bessie and Elsie are playing a game on a binary array $a$ of length $n$.

The players alternate turns, with Bessie moving first. On Bessie's turn, she chooses two adjacent elements $x$ and $y$ and replaces them with the single value $\max(x,y)$.

On Elsie's turn, she chooses two adjacent elements $x$ and $y$ and replaces them with the single value $\min(x,y)$.

After each move, the length of the array decreases by $1$. The game ends when only one element remains. Bessie wins if the final element is $1$, and Elsie wins if the final element is $0$.

Assuming both players play optimally, determine who wins.

贝茜和埃尔西正在一个长度为 $n$ 的二进制数组 $a$ 上进行一场游戏。

两名玩家轮流行动，贝茜先手。在贝茜的回合中，她选择两个相邻元素 $x$ 和 $y$，并将它们替换为单个值 $\max(x,y)$。

在埃尔西的回合中，她选择两个相邻元素 $x$ 和 $y$，并将它们替换为单个值 $\min(x,y)$。

每次操作后，数组长度减少 $1$。当数组中仅剩一个元素时，游戏结束。若最终元素为 $1$，则贝茜获胜；若最终元素为 $0$，则埃尔西获胜。

假设双方均以最优策略进行游戏，请判断谁将获胜。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($2 \leq n \leq 100$).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i \leq 1$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 500$）。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$2 \leq n \leq 100$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \leq a_i \leq 1$）。

For each test case, you should output the name of who wins on a new line.

对于每个测试用例，您应在新的一行输出获胜者的名字。

For the first test case, Bessie can guarantee a win. One possible game is as follows: $$ [\color{red}{1},\color{red}{0},1,0,1] \to [1,\color{red}{1},\color{red}{0},1] \to [\color{red}{1},\color{red}{0},1] \to [\color{red}{1},\color{red}{1}] \to [1]. $$ The final value is $1$, so Bessie wins (the red highlight denotes the two adjacent elements picked on that turn).

For the second test case, no matter which move Bessie makes, Elsie can make the final value $0$. Therefore, Elsie wins.

For the third test case, one possible winning game for Bessie is: $$ [1,\color{red}{1},\color{red}{0},0] \to [1,\color{red}{1},\color{red}{0}] \to [\color{red}{1},\color{red}{0}] \to [1]. $$ The final value is $1$, so Bessie wins.

对于第一个测试用例，贝西可以确保获胜。一种可能的游戏过程如下：

\[\color{red}{1},\color{red}{0},1,0,1\] \to \[1,\color{red}{1},\color{red}{0},1\] \to \[\color{red}{1},\color{red}{0},1\] \to \[\color{red}{1},\color{red}{1}\] \to \[1\].

最终值为 $1$，因此贝西获胜（红色高亮表示该回合所选的两个相邻元素）。

对于第二个测试用例，无论贝西如何操作，埃尔西都能使最终值为 $0$。因此，埃尔西获胜。

对于第三个测试用例，贝西的一种获胜策略如下：

\[1,\color{red}{1},\color{red}{0},0\] \to \[1,\color{red}{1},\color{red}{0}\] \to \[\color{red}{1},\color{red}{0}\] \to \[1\].

最终值为 $1$，因此贝西获胜。