201231: [AtCoder]ARC123 B - Increasing Triples

Problem Statement

Given are three sequences of $N$ integers each: $A = (A_1, \ldots, A_N),\,B = (B_1, \ldots, B_N),\,C = (C_1, \ldots, C_N)$.

You can permute each of these sequences in any way you like. Find the maximum possible number of indices $i$ such that $A_i < B_i < C_i$ after permuting them.

Constraints

• $1\leq N\leq 10^5$
• $1\leq A_i, B_i, C_i\leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\ldots$ $A_N$
$B_1$ $B_2$ $\ldots$ $B_N$
$C_1$ $C_2$ $\ldots$ $C_N$

Output

Print the answer.

Sample Input 1

5
9 6 14 1 8
2 10 3 12 11
15 13 5 7 4

Sample Output 1

3

We should permute them as follows:

• $A = (1,6,8,9,14)$,
• $B = (3,2,10,12,11)$,
• $C = (4,7,15,13,5)$.

Then, we will have three indices $i$ ($i = 1, 3, 4$) such that $A_i < B_i < C_i$.

Sample Input 2

1
10
20
30

Sample Output 2

1

Sample Input 3

3
1 1 1
1 1 2
2 2 2

Sample Output 3

0