Cow Checkups

문제

Farmer John's $NN$ ($1\le N\le 5\cdot {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 5\; \backslash cdot\; 10^5$) cows are standing in a line, with cow $11$ at the front of the line and cow $NN$ at the back of the line. FJ's cows also come in many different species. He denotes each species with an integer from $11$ to $NN$. The $ii$'th cow from the front of the line is of species $a_{i}a\_i$ ($1\le a_i\le N1\; \backslash leq\; a\_i\; \backslash leq\; N$).

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 $ii$'th cow in the line, only if it is species $b_{i}b\_i$ ($1\le b_i\le N1\; \backslash leq\; b\_i\; \backslash leq\; N$).

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

• Select two integers $ll$ and $rr$ such that $1\le l\le r\le N1\; \backslash leq\; l\; \backslash le\; r\; \backslash leq\; N$. Reverse the order of the cows that are between the $ll$-th cow and the $rr$-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 $N(N+1)\mathrm{/}2N(N+1)/2$ possible operations.

입력

The first line contains an integer $NN$.

The second line contains $a_1,a_2,\dots ,a_{N}a\_1,\; a\_2,\; \backslash ldots,\; a\_N$.

The third line contains $b_1,b_2,\dots ,b_{N}b\_1,\; b\_2,\; \backslash ldots,\; b\_N$.

출력

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