Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

data structures

greedy

sortings

*1400

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Digital Logarithm

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet'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.

Example

Input

411100041 2 3 43 1 4 232 9 31 100 91075019 709259 5 611271314 9024533 81871864 9 3 6 48659503 2 371245467 6 7 37376159 8 364036498 52295554 169

Output

2 0 2 18

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 $$$b_2$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/18/2024 12:03:10 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|