CF1738A.Glory Addicts

The hero is addicted to glory, and is fighting against a monster.

The hero has $n$ skills. The $i$-th skill is of type $a_i$ (either fire or frost) and has initial damage $b_i$.

The hero can perform all of the $n$ skills in any order (with each skill performed exactly once). When performing each skill, the hero can play a magic as follows:

• If the current skill immediately follows another skill of a different type, then its damage is doubled.

In other words,

1. If a skill of type fire and with initial damage $c$ is performed immediately after a skill of type fire, then it will deal $c$ damage;
2. If a skill of type fire and with initial damage $c$ is performed immediately after a skill of type frost, then it will deal $2c$ damage;
3. If a skill of type frost and with initial damage $c$ is performed immediately after a skill of type fire, then it will deal $2c$ damage;
4. If a skill of type frost and with initial damage $c$ is performed immediately after a skill of type frost , then it will deal $c$ damage.

Your task is to find the maximum damage the hero can deal.

英雄沉溺于荣耀，正与一只怪物战斗。

英雄拥有 $n$ 个技能。第 $i$ 个技能的类型为 $a_i$（火系或冰系），初始伤害值为 $b_i$。

英雄可以以任意顺序施展全部 $n$ 个技能（每个技能恰好施展一次）。每次施展一个技能时，英雄可施放如下魔法：

• 若当前技能紧接在另一个不同类型的技能之后施展，则其伤害值翻倍。

换言之：

1. 若一个火系技能（初始伤害为 $c$）紧接在另一个火系技能之后施展，则造成 $c$ 点伤害；
2. 若一个火系技能（初始伤害为 $c$）紧接在另一个冰系技能之后施展，则造成 $2c$ 点伤害；
3. 若一个冰系技能（初始伤害为 $c$）紧接在另一个火系技能之后施展，则造成 $2c$ 点伤害；
4. 若一个冰系技能（初始伤害为 $c$）紧接在另一个冰系技能之后施展，则造成 $c$ 点伤害。

你的任务是求出英雄所能造成的最大总伤害值。

Each test contains multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 10^5$) — the number of test cases. The following lines contain the description of each test case.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 10^5$), indicating the number of skills.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \leq a_i \leq 1$), where $a_i$ indicates the type of the $i$-th skill. Specifically, the $i$-th skill is of type fire if $a_i = 0$, and of type frost if $a_i = 1$.

The third line of each test case contains $n$ integers $b_1, b_2, \dots, b_n$ ($1 \leq b_i \leq 10^9$), where $b_i$ indicates the initial damage of the $i$-th skill.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 10^5$），表示测试用例的数量。接下来的若干行描述每个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 10^5$），表示技能的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \leq a_i \leq 1$），其中 $a_i$ 表示第 $i$ 个技能的类型：若 $a_i = 0$，则该技能为火焰系；若 $a_i = 1$，则该技能为寒冰系。

每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$1 \leq b_i \leq 10^9$），其中 $b_i$ 表示第 $i$ 个技能的初始伤害值。

保证所有测试用例中 $n$ 的总和不超过 $10^5$。

For each test case, output the maximum damage the hero can deal.

对于每个测试用例，输出英雄所能造成的最大伤害。

In the first test case, we can order the skills by $[3, 1, 4, 2]$, and the total damage is $100 + 2 \times 1 + 2 \times 1000 + 10 = 2112$.

In the second test case, we can order the skills by $[1, 4, 2, 5, 3, 6]$, and the total damage is $3 + 2 \times 6 + 2 \times 4 + 2 \times 7 + 2 \times 5 + 2 \times 8 = 63$.

In the third test case, we can order the skills by $[1, 2, 3]$, and the total damage is $1000000000 + 1000000000 + 1000000000 = 3000000000$.

In the fourth test case, there is only one skill with initial damage $1$, so the total damage is $1$.

在第一个测试用例中，我们可以将技能按 $[3, 1, 4, 2]$ 的顺序排列，总伤害为 $100 + 2 \times 1 + 2 \times 1000 + 10 = 2112$。

在第二个测试用例中，我们可以将技能按 $[1, 4, 2, 5, 3, 6]$ 的顺序排列，总伤害为 $3 + 2 \times 6 + 2 \times 4 + 2 \times 7 + 2 \times 5 + 2 \times 8 = 63$。

在第三个测试用例中，我们可以将技能按 $[1, 2, 3]$ 的顺序排列，总伤害为 $1000000000 + 1000000000 + 1000000000 = 3000000000$。

在第四个测试用例中，仅有一个初始伤害为 $1$ 的技能，因此总伤害为 $1$。