C. Digital Logarithmtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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?InputThe 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.OutputFor each testcase, print the smallest number of operations required to make a and b similar to each other.ExampleInput
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 169Output
2
0
2
18
NoteIn 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.
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
2 0 2 18 
['data structures', 'greedy', 'sortings', '*1400']