Score : $200$ points

Problem Statement

You are given integer sequences, each of length $N$: $A = (A_1, A_2, \dots, A_N)$ and $B = (B_1, B_2, \dots, B_N)$. All elements of $A$ are different. All elements of $B$ are different, too.

Print the following two values.

1. The number of integers contained in both $A$ and $B$, appearing at the same position in the two sequences. In other words, the number of integers $i$ such that $A_i = B_i$.
2. The number of integers contained in both $A$ and $B$, appearing at different positions in the two sequences. In other words, the number of pairs of integers $(i, j)$ such that $A_i = B_j$ and $i \neq j$.

Constraints

• $1 \leq N \leq 1000$
• $1 \leq A_i \leq 10^9$
• $1 \leq B_i \leq 10^9$
• $A_1, A_2, \dots, A_N$ are all different.
• $B_1, B_2, \dots, B_N$ are all different.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

$B_1$ $B_2$ $\dots$ $B_N$

Output

Print the answers in two lines: the answer to1. in the first line, and the answer to2. in the second line.

4
1 3 5 2
2 3 1 4

1
2

There is one integer contained in both $A$ and $B$, appearing at the same position in the two sequences: $A_2 = B_2 = 3$. There are two integers contained in both $A$ and $B$, appearing at different positions in the two sequences: $A_1 = B_3 = 1$ and $A_4 = B_1 = 2$.

3
1 2 3
4 5 6

0
0

In both 1. and 2., no integer satisfies the condition.

7
4 8 1 7 9 5 6
3 5 1 7 8 2 6

3
2