Description

Farmer John's $N$ ($1 \leq N \leq 5 \cdot 10^5$) cows are standing in a line, with cow $1$ at the front of the line and cow $N$ at the back of the line. FJ's cows also come in many different species. He denotes each species with an integer from $1$ to $N$. The $i$'th cow from the front of the line is of species $a_i$ ($1 \leq a_i \leq N$).

FJ is taking his cows to a checkup at a local bovine hospital. However, the bovine veterinarian is very picky and wants to perform a checkup on the $i$'th cow in the line, only if it is species $b_i$ ($1 \leq b_i \leq N$).

FJ is lazy and does not want to completely reorder his cows. He will perform the following operation exactly once.

• Select two integers $l$ and $r$ such that $1 \leq l \le r \leq N$. Reverse the order of the cows that are between the $l$-th cow and the $r$-th cow in the line, inclusive.

FJ wants to measure how effective this approach is. Find the sum of the number of cows that are checked by the veterinarian over all $N(N+1)/2$ possible operations.

Input Format

The first line contains an integer $N$.

The second line contains $a_1, a_2, \ldots, a_N$.

The third line contains $b_1, b_2, \ldots, b_N$.

Output Format

Output one line with the sum of the number of cows that are checked by the veterinarian over all possible operations.

3
1 3 2
3 2 1

3

3
1 2 3
1 2 3

12

7
1 3 2 2 1 3 2
3 2 2 1 2 3 1

60

Hint

For Sample 1:

If FJ chooses ($l=1,r=1$), ($l=2,r=2$), or ($l=3,r=3$) then no cows will be checked. Note that those operations do not modify the location of the cows.

The following operations result in one cow being checked.

• $l=1,r=2$: FJ reverses the order of the first and second cows so the species of each cow in the new lineup will be $[3,1,2]$. The first cow will be checked.
• $l=2,r=3$: FJ reverses the order of the second and third cows so the species of each cow in the new lineup will be $[1,2,3]$. The second cow will be checked.
• $l=1,r=3$: FJ reverses the order of the first, second, and third cows so the species of each cow in the new lineup will be $[2,3,1]$. The third cow will be checked.

The total number of cows checked over all six operations is $0+0+0+1+1+1=3$.

For Sample 2:

There are three possible operations that cause $3$ cows to be checked: ($l=1,r=1$), ($l=2,r=2$), and ($l=3,r=3$). The remaining operations each result in $1$ cow being checked. The total number of cows checked over all six operations is $3+3+3+1+1+1=12$.

SCORING:

• Input 4: $N\le 100$
• Input 5: $N\le 5000$
• Inputs 6-9: $a_i, b_i$ are all generated uniformly at random in the range $[1,N]$
• Inputs 10-15: $a_i, b_i$ are all generated uniformly at random in the range $[1,2]$
• Inputs 16-23: No additional constraints.