Bessie's Function

문제

Bessie has a special function $f(x)f(x)$ that takes as input an integer in $[1,N][1,\; N]$ and returns an integer in $[1,N][1,\; N]$ ($1\le N\le 2\cdot {10}^{5}1\; \backslash le\; N\; \backslash le\; 2\; \backslash cdot\; 10^5$). Her function $f(x)f(x)$ is defined by $NN$ integers $a_1\dots a_{N}a\_1\; \backslash ldots\; a\_N$ where $f(x)=a_{x}f(x)\; =\; a\_x$ ($1\le a_i\le N1\; \backslash le\; a\_i\; \backslash le\; N$).

Bessie wants this function to be idempotent. In other words, it should satisfy $f(f(x))=f(x)f(f(x))\; =\; f(x)$ for all integers $x\in [1,N]x\; \backslash in\; [1,\; N]$.

For a cost of $c_{i}c\_i$, Bessie can change the value of $a_{i}a\_i$ to any integer in $[1,N][1,\; N]$ ($1\le c_i\le {10}^{9}1\; \backslash le\; c\_i\; \backslash le\; 10^9$). Determine the minimum total cost Bessie needs to make $f(x)f(x)$ idempotent.

입력

The first line contains $NN$.

The second line contains $NN$ space-separated integers $a_1,a_2,\dots ,a_{N}a\_1,a\_2,\backslash dots,a\_N$.

The third line contains $NN$ space-separated integers $c_1,c_2,\dots ,c_{N}c\_1,c\_2,\backslash dots,c\_N$.

출력

Output the minimum total cost Bessie needs to make $f(x)f(x)$ idempotent.

5
2 4 4 5 3
1 1 1 1 1

3

8
1 2 5 5 3 3 4 4
9 9 2 5 9 9 9 9

7