CF1728C Digital Logarithm

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.

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 $ .