Digital Logarithm

2000ms

262144K

Description:

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:

pick some integer $$$i$$$ from $$$1$$$ to $$$n$$$;
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?

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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

Sample Input:

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

Sample Output:

Note:

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 $$$b_2$$$.

Informação

Provedor Codeforces

Código CF1728C