D. Mouse Hunt

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Medicine faculty of Berland State University has just finished their admission campaign. As usual, about 80%80% of applicants are girls and majority of them are going to live in the university dormitory for the next 44 (hopefully) years.

The dormitory consists of nn rooms and a single mouse! Girls decided to set mouse traps in some rooms to get rid of the horrible monster. Setting a trap in room number ii costs cici burles. Rooms are numbered from 11 to nn.

Mouse doesn't sit in place all the time, it constantly runs. If it is in room ii in second tt then it will run to room aiai in second t+1t+1 without visiting any other rooms inbetween (i=aii=ai means that mouse won't leave room ii). It's second 00 in the start. If the mouse is in some room with a mouse trap in it, then the mouse get caught into this trap.

That would have been so easy if the girls actually knew where the mouse at. Unfortunately, that's not the case, mouse can be in any room from 11 to nn at second 00.

What it the minimal total amount of burles girls can spend to set the traps in order to guarantee that the mouse will eventually be caught no matter the room it started from?

Input

The first line contains as single integers nn (1≤n≤2⋅1051≤n≤2⋅105) — the number of rooms in the dormitory.

The second line contains nn integers c1,c2,…,cnc1,c2,…,cn (1≤ci≤1041≤ci≤104) — cici is the cost of setting the trap in room number ii.

The third line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤n1≤ai≤n) — aiai is the room the mouse will run to the next second after being in room ii.

Output

Print a single integer — the minimal total amount of burles girls can spend to set the traps in order to guarantee that the mouse will eventually be caught no matter the room it started from.

Examples

input

Copy

5
1 2 3 2 10
1 3 4 3 3

output

Copy

3

input

Copy

4
1 10 2 10
2 4 2 2

output

Copy

10

input

Copy

7
1 1 1 1 1 1 1
2 2 2 3 6 7 6

output

Copy

2

Note

In the first example it is enough to set mouse trap in rooms 11 and 44. If mouse starts in room 11 then it gets caught immideately. If mouse starts in any other room then it eventually comes to room 44.

In the second example it is enough to set mouse trap in room 22. If mouse starts in room 22 then it gets caught immideately. If mouse starts in any other room then it runs to room 22 in second 11.

Here are the paths of the mouse from different starts from the third example:

• 1→2→2→…1→2→2→…;
• 2→2→…2→2→…;
• 3→2→2→…3→2→2→…;
• 4→3→2→2→…4→3→2→2→…;
• 5→6→7→6→…5→6→7→6→…;
• 6→7→6→…6→7→6→…;
• 7→6→7→…7→6→7→…;

So it's enough to set traps in rooms 22 and 66.

題意：給你若干個房間，還有一隻老鼠穿梭其中，老鼠的起始位置是隨意的，假如老鼠在第i個房間，則它下次的目的地是ai，然後你可以在若干個房間裡設定老鼠夾來捕捉老鼠，每個房間放置老鼠夾的代價是bi，你可以在任意房間放老鼠夾，但是你必須要使得不管老鼠從哪裡出發都能捉到老鼠，問你花費的總代價是多少？

題解：很容易想到的是，若一些房間構成了一個環，則只用在這個環中找一個房間放置老鼠夾就行了，因此我們可以對於每個環找出花費代價最小的房間設定老鼠夾。當然有些還上會存在一些鏈，因此我們可以用標記陣列巧妙地標記不屬於環內的房間即可，這些房間一定不用放置老鼠夾的，具體見程式碼。

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define ll long long
#define maxn 200005
int n,a[maxn],b[maxn],ans,flag[maxn];
int main(void)
{
	int cnt=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]);
	for(int i=1;i<=n;i++)
		scanf("%d",&b[i]);
	for(int i=1;i<=n;i++)
	{
		if(flag[i]) continue;
		int p=i; cnt++;
		while(1)
		{
			flag[p]=cnt;p=b[p];
			if(flag[p]==cnt)
			{
				int des=p;
				int t=b[des];
				int tmp=a[des];
				while(t!=des)
					tmp=min(tmp,a[t]),t=b[t];
				ans+=tmp;
				break;
			}
			else if(flag[p] && flag[p]!=cnt)
				break;
		}
	}
	printf("%d\n",ans);
	return 0;
}