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# [Solution] Digital Logarithm Codeforces Solution

C. Digital Logarithm
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let's define $f\left(x\right)$ 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 $f\left({a}_{i}\right)$ to ${a}_{i}$ or $f\left({b}_{i}\right)$ 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.

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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.

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 ${b}_{2}$.