Score : $300$ points

Problem Statement

Given are three sequences of length $N$ each: $A = (A_1, A_2, \dots, A_N)$, $B = (B_1, B_2, \dots, B_N)$, and $C = (C_1, C_2, \dots, C_N)$, consisting of integers between $1$ and $N$ (inclusive).

How many pairs $(i, j)$ of integers between $1$ and $N$ (inclusive) satisfy $A_i = B_{C_j}$?

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i, B_i, C_i \leq N$
• All values in input are integers.

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 number of pairs $(i, j)$ such that $A_i = B_{C_j}$.

3
1 2 2
3 1 2
2 3 2

4

Four pairs satisfy the condition: $(1, 1), (1, 3), (2, 2), (3, 2)$.

4
1 1 1 1
1 1 1 1
1 2 3 4

16

All the pairs satisfy the condition.

3
2 3 3
1 3 3
1 1 1

0

No pair satisfies the condition.