CF1401B.Ternary Sequence

You are given two sequences $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$. Each element of both sequences is either $0$, $1$ or $2$. The number of elements $0$, $1$, $2$ in the sequence $a$ is $x_1$, $y_1$, $z_1$ respectively, and the number of elements $0$, $1$, $2$ in the sequence $b$ is $x_2$, $y_2$, $z_2$ respectively.

You can rearrange the elements in both sequences $a$ and $b$ however you like. After that, let's define a sequence $c$ as follows:

c_i = \begin{cases} a_i b_i & \mbox{if }a_i \gt b_i \\ 0 & \mbox{if }a_i = b_i \\ -a_i b_i & \mbox{if }a_i \lt b_i \end{cases}

You'd like to make $\sum_{i=1}^n c_i$ (the sum of all elements of the sequence $c$) as large as possible. What is the maximum possible sum?

给你两个序列 $a_1, a_2, \dots, a_n$ 和 $b_1, b_2, \dots, b_n$。这两个序列中的每个元素均为 $0$、$1$ 或 $2$。序列 $a$ 中元素 $0$、$1$、$2$ 的个数分别为 $x_1$、$y_1$、$z_1$；序列 $b$ 中元素 $0$、$1$、$2$ 的个数分别为 $x_2$、$y_2$、$z_2$。

你可以任意重排序列 $a$ 和 $b$ 中的元素。重排后，定义序列 $c$ 如下：

c_i = \begin{cases} a_i b_i & \mbox{若 }a_i \gt b_i \\ 0 & \mbox{若 }a_i = b_i \\ -a_i b_i & \mbox{若 }a_i \lt b_i \end{cases}

你希望使 $\sum_{i=1}^n c_i$（即序列 $c$ 所有元素之和）尽可能大。该和的最大可能值是多少？

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

Each test case consists of two lines. The first line of each test case contains three integers $x_1$, $y_1$, $z_1$ ($0 \le x_1, y_1, z_1 \le 10^8$) — the number of $0$-s, $1$-s and $2$-s in the sequence $a$.

The second line of each test case also contains three integers $x_2$, $y_2$, $z_2$ ($0 \le x_2, y_2, z_2 \le 10^8$; $x_1 + y_1 + z_1 = x_2 + y_2 + z_2 \gt 0$) — the number of $0$-s, $1$-s and $2$-s in the sequence $b$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例由两行组成。每个测试用例的第一行包含三个整数 $x_1$、$y_1$、$z_1$（$0 \le x_1, y_1, z_1 \le 10^8$）—— 分别表示序列 $a$ 中 $0$、$1$ 和 $2$ 的个数。

每个测试用例的第二行也包含三个整数 $x_2$、$y_2$、$z_2$（$0 \le x_2, y_2, z_2 \le 10^8$；且满足 $x_1 + y_1 + z_1 = x_2 + y_2 + z_2 \gt 0$）—— 分别表示序列 $b$ 中 $0$、$1$ 和 $2$ 的个数。

For each test case, print the maximum possible sum of the sequence $c$.

对于每个测试用例，输出序列 $c$ 的最大可能和。

In the first sample, one of the optimal solutions is:

$a = {2, 0, 1, 1, 0, 2, 1}$

$b = {1, 0, 1, 0, 2, 1, 0}$

$c = {2, 0, 0, 0, 0, 2, 0}$

In the second sample, one of the optimal solutions is:

$a = {0, 2, 0, 0, 0}$

$b = {1, 1, 0, 1, 0}$

$c = {0, 2, 0, 0, 0}$

In the third sample, the only possible solution is:

$a = {2}$

$b = {2}$

$c = {0}$

在第一个样例中，一个最优解为：

$a = \{2, 0, 1, 1, 0, 2, 1\}$

$b = \{1, 0, 1, 0, 2, 1, 0\}$

$c = \{2, 0, 0, 0, 0, 2, 0\}$

在第二个样例中，一个最优解为：

$a = \{0, 2, 0, 0, 0\}$

$b = \{1, 1, 0, 1, 0\}$

$c = \{0, 2, 0, 0, 0\}$

在第三个样例中，唯一可能的解为：

$a = \{2\}$

$b = \{2\}$

$c = \{0\}$