Digital Logarithm

### 题目大意 我们定义 $f(x)$ 表示取出 $x$ 在**十进制**下的位数。( 如 $f(114514) = 6, \; f(998244353) = 9$ )。形式化讲，就是 $f(x) = \lfloor \log_{10} x \rfloor + 1$。 给定两个数组 $a$ 和 $b$，求执行若干次以下操作后使得 $a$ 和 $b$ **排序后**相等的最小操作次数。 操作方法如下： - 选择一个下标 $i$，将 $a_i$ 赋值为 $f(a_i)$ **或者**将 $b_i$ 赋值为 $f(b_i)$。 ### 输入格式 第一行一个整数 $T \; (1 \leqslant T \leqslant 10^4)$ 表示测试样例组数。 对于每组测试样例，第一行为一个整数 $n \; (1 \leqslant n \leqslant 2 \cdot 10^5)$ 表示数组长度。 接下来的两行分别有 $n$ 个整数，表示数组 $a$ 和 $b \; (1 \leqslant a_i,b_i < 10^9)$。 数据保证 $\sum n \leqslant 2 \cdot 10^5$ ### 输出格式 对于每组测试样例，输出包含一行一个整数，表示最小操作次数。 $Translated \; by \; Zigh$

Let's define $ f(x) $ for a positive integer $ x $ as the length of the base-10 representation of $ x $ without leading zeros. I like to call it a digital logarithm. Similar to a digital root, if you are familiar with that. You are given two arrays $ a $ and $ b $ , each containing $ n $ positive integers. In one operation, you do the following: 1. pick some integer $ i $ from $ 1 $ to $ n $ ; 2. assign either $ f(a_i) $ to $ a_i $ or $ f(b_i) $ to $ b_i $ . Two arrays are considered similar to each other if you can rearrange the elements in both of them, so that they are equal (e. g. $ a_i = b_i $ for all $ i $ from $ 1 $ to $ n $ ). What's the smallest number of operations required to make $ a $ and $ b $ similar to each other?

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of testcases. The first line of the testcase contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the number of elements in each of the arrays. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i < 10^9 $ ). The third line contains $ n $ integers $ b_1, b_2, \dots, b_n $ ( $ 1 \le b_j < 10^9 $ ). The sum of $ n $ over all testcases doesn't exceed $ 2 \cdot 10^5 $ .

For each testcase, print the smallest number of operations required to make $ a $ and $ b $ similar to each other.

4
1
1
1000
4
1 2 3 4
3 1 4 2
3
2 9 3
1 100 9
10
75019 709259 5 611271314 9024533 81871864 9 3 6 4865
9503 2 371245467 6 7 37376159 8 364036498 52295554 169

2
0
2
18

In the first testcase, you can apply the digital logarithm to $ b_1 $ twice. In the second testcase, the arrays are already similar to each other. In the third testcase, you can first apply the digital logarithm to $ a_1 $ , then to $ b_2 $ .