CF2230A.Optimal Purchase

You have a group of $n$ students who need access to an online course. Two types of access keys are available in the store:

1. Individual key: costs $a$ dollars and gives access to one student.
2. Group key: costs $b$ dollars and gives access to a group of up to three students inclusive.

A group key can also be used for fewer students (one or two), and its price does not change.

Your task is to determine the minimum amount of money needed to provide access to the online course for all $n$ students.

你有一组 $n$ 名学生需要访问一门在线课程。商店中提供两种类型的访问密钥：

1. 单人密钥：花费 $a$ 美元，可供一名学生使用。
2. 团体密钥：花费 $b$ 美元，可供最多三名学生（含三名）共同使用。

团体密钥也可供较少的学生（一名或两名）使用，且其价格不变。

你的任务是确定为全部 $n$ 名学生提供在线课程访问权限所需的最少金额。

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

Each test case consists of one line containing three integers $n, a, b$ ($1 \le n, a, b \le 10^8$) — the number of students, the cost of an individual key, and the cost of a group key.

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

每个测试用例由一行组成，包含三个整数 $n, a, b$（$1 \le n, a, b \le 10^8$）—— 学生人数、单把钥匙的费用以及团体钥匙的费用。

For each test case, output one integer — the minimum amount of money needed to provide access to the online course for all $n$ students.

对于每个测试用例，输出一个整数——为全部 $n$ 名学生提供在线课程访问权限所需的最少金额。

In the first example, you can buy $1$ group key and $2$ individual keys.

In the second example, you can buy $4$ individual keys.

In the third example, you can buy $1$ group key.

In the fourth example, you can buy $1$ individual key.

在第一个例子中，你可以购买 $1$ 个团体密钥和 $2$ 个单独密钥。

在第二个例子中，你可以购买 $4$ 个单独密钥。

在第三个例子中，你可以购买 $1$ 个团体密钥。

在第四个例子中，你可以购买 $1$ 个单独密钥。