A13724 | 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:

$c_i = \begin{cases} a_i b_i & \mbox{if }a_i > b_i \\ 0 & \mbox{if }a_i = b_i \\ -a_i b_i & \mbox{if }a_i < b_i \end{cases}$

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?

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 $x_2$ , $y_2$ , $z_2$ ( $0 \le x_2, y_2, z_2 \le 10^8$ ; $x_1 + y_1 + z_1 = x_2 + y_2 + z_2 > 0$ ) — the number of $0$ -s, $1$ -s and $2$ -s in the sequence $b$ .

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