#P1728C. Digital Logarithm

Digital Logarithm

Description

Let's define f(x)f(x) for a positive integer xx as the length of the base-10 representation of xx 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 aa and bb, each containing nn positive integers. In one operation, you do the following:

  1. pick some integer ii from 11 to nn;
  2. assign either f(ai)f(a_i) to aia_i or f(bi)f(b_i) to bib_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. ai=bia_i = b_i for all ii from 11 to nn).

What's the smallest number of operations required to make aa and bb similar to each other?

The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of testcases.

The first line of the testcase contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5) — the number of elements in each of the arrays.

The second line contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai<1091 \le a_i < 10^9).

The third line contains nn integers b1,b2,,bnb_1, b_2, \dots, b_n (1bj<1091 \le b_j < 10^9).

The sum of nn over all testcases doesn't exceed 21052 \cdot 10^5.

For each testcase, print the smallest number of operations required to make aa and bb similar to each other.

Input

The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of testcases.

The first line of the testcase contains a single integer nn (1n21051 \le n \le 2 \cdot 10^5) — the number of elements in each of the arrays.

The second line contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai<1091 \le a_i < 10^9).

The third line contains nn integers b1,b2,,bnb_1, b_2, \dots, b_n (1bj<1091 \le b_j < 10^9).

The sum of nn over all testcases doesn't exceed 21052 \cdot 10^5.

Output

For each testcase, print the smallest number of operations required to make aa and bb similar to each other.

Samples

样例输入 1

<div class="test-example-line test-example-line-even test-example-line-0">4</div><div class="test-example-line test-example-line-odd test-example-line-1">1</div><div class="test-example-line test-example-line-odd test-example-line-1">1</div><div class="test-example-line test-example-line-odd test-example-line-1">1000</div><div class="test-example-line test-example-line-even test-example-line-2">4</div><div class="test-example-line test-example-line-even test-example-line-2">1 2 3 4</div><div class="test-example-line test-example-line-even test-example-line-2">3 1 4 2</div><div class="test-example-line test-example-line-odd test-example-line-3">3</div><div class="test-example-line test-example-line-odd test-example-line-3">2 9 3</div><div class="test-example-line test-example-line-odd test-example-line-3">1 100 9</div><div class="test-example-line test-example-line-even test-example-line-4">10</div><div class="test-example-line test-example-line-even test-example-line-4">75019 709259 5 611271314 9024533 81871864 9 3 6 4865</div><div class="test-example-line test-example-line-even test-example-line-4">9503 2 371245467 6 7 37376159 8 364036498 52295554 169</div>

样例输出 1

2
0
2
18

Note

In the first testcase, you can apply the digital logarithm to b1b_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 a1a_1, then to b2b_2.