Medicine faculty of Berland State University has just finished their admission campaign. As usual, about 80\% of applicants are girls and majority of them are going to live in the university dormitory for the next 4 (hopefully) years.

The dormitory consists of n 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 i costs c_i burles. Rooms are numbered from 1 to n.

Mouse doesn't sit in place all the time, it constantly runs. If it is in room i in second t then it will run to room a_i in second t + 1 without visiting any other rooms inbetween (i = a_i means that mouse won't leave room i). It's second 0 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 1 to n at second 0.

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 n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of rooms in the dormitory.

The second line contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 10^4) — c_i is the cost of setting the trap in room number i.

The third line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — a_i is the room the mouse will run to the next second after being in room i.

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

5
1 2 3 2 10
1 3 4 3 3


Output

3


Input

4
1 10 2 10
2 4 2 2


Output

10


Input

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


Output

2

Note

In the first example it is enough to set mouse trap in rooms 1 and 4. If mouse starts in room 1 then it gets caught immideately. If mouse starts in any other room then it eventually comes to room 4.

In the second example it is enough to set mouse trap in room 2. If mouse starts in room 2 then it gets caught immideately. If mouse starts in any other room then it runs to room 2 in second 1.

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

  * 1 → 2 → 2 → ...; 
  * 2 → 2 → ...; 
  * 3 → 2 → 2 → ...; 
  * 4 → 3 → 2 → 2 → ...; 
  * 5 → 6 → 7 → 6 → ...; 
  * 6 → 7 → 6 → ...; 
  * 7 → 6 → 7 → ...; 



So it's enough to set traps in rooms 2 and 6.

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class codeforces 
{ 
   static class Student{
       int x,y;//z;
        Student(int x,int y){
            this.x=x;
            this.y=y;
            //this.z=z;
        }
    }
    static int prime[];
    static void sieveOfEratosthenes(int n) 
    { 
        // Create a boolean array "prime[0..n]" and initialize 
        // all entries it as true. A value in prime[i] will 
        // finally be false if i is Not a prime, else true. 
        int pos=0;
        prime= new int[n+1]; 
        for(int p = 2; p*p <=n; p++) 
        { 
            // If prime[p] is not changed, then it is a prime 
            if(prime[p] == 0)
            { 
                // Update all multiples of p
                prime[p]=p;
                for(int i = p*p; i <= n; i += p)
                    if(prime[i]==0)
                    prime[i] = p; 
            } 
        } 
    }
static    class Sortbyroll implements Comparator<Student> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(Student c, Student b) 
    {
        return c.x-b.x;
    } 
} 
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
 
    static class Edge{
        int a,b;
        Edge(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    static class Trie{
        HashMap<Character,Trie>map;
         int c;
        Trie(){
            map=new HashMap<>();
            //z=null;
            //o=null;
            c=0;
        }
    }
    //static long ans;
    static int parent[];
    static int rank[];
    static int b[];
    static int h[];
    static int ho[][];
    static int seg[];
    //static int pos;
    //static long mod=1000000000+7;
    //static int dp[][];
    static HashMap<String,Integer>map;
    static PriorityQueue<Student>q=new PriorityQueue<>();
    //static Stack<Integer>st;
   // static ArrayList<Character>ans;
    static ArrayList<ArrayList<Integer>>adj;
    //static ArrayList<ArrayList<Integer>>tr;
    static ArrayList<HashMap<Long,Student>>map1;
    static ArrayList<HashMap<Long,Long>>map2;
    //static long ans;
    static int pos;
    static Trie root;
    static long fac[];
    static int s,d;
    static int gw,gb;
    static long mod=(long)(998244353);
    static long ans1;
    static long ans2;
    static void solve()throws IOException{
        FastReader sc=new FastReader();
        int t,n,m,i,x,y,ans=0;
        //long ans;
        n=sc.nextInt();
        //int a[]=new int[n];
        b=new int[n];
        h=new int[n];
        int c[]=new int[n];
        int a[]=new int[n];
        adj=new ArrayList<>();
        for(i=0;i<n;i++)
            c[i]=sc.nextInt();
        for(i=0;i<n;i++)
            adj.add(new ArrayList<>());
        for(i=0;i<n;i++){
            x=sc.nextInt()-1;
            a[i]=x;
            //y=sc.nextInt()-1;
            adj.get(i).add(x);
            adj.get(x).add(i);
        }
        for(i=0;i<n;i++){
            if(h[i]!=0)
                continue;
            s=i;
            d=i;
            dfs(-1,i,c);
            ans1=c[d];
            while(s!=d){
                ans1=Math.min(ans1,c[s]);
                s=a[s];
            }
            ans+=ans1;
        }
        System.out.println(ans);
    }
    static void dfs(int p,int c,int co[]){
        if(h[c]==1){
            s=p;
            d=c;
            return;
        }
        //b[c]=1;
        h[c]=1;
        //ans1=Math.min(ans1,co[c]);
        for(Integer x:adj.get(c)){
            if(x==p)
                continue;
            dfs(c,x,co);
        }
        //b[c]=0;
    }

    static void dfs2(int p,int c,long dp1[][],long dp[]){
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs2(c,x,dp1,dp);
            dp[c]=Math.max(dp[c],dp[x]);
            if(dp1[c][0]==Long.MIN_VALUE)
                dp1[c][0]=dp[x];
            else if(dp1[c][0]<=dp[x]){
                dp1[c][1]=dp1[c][0];
                dp1[c][0]=dp[x];
            }
            else
                dp1[c][1]=Math.max(dp1[c][1],dp[x]);
        }
    }
    static void dfs(int p,int c,int a[],long dp[]){
        dp[c]=a[c];
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs(c,x,a,dp);
            dp[c]+=dp[x];
        }
    }
    static void dfs(int x,int y,char f[][],int n,int m){
        f[x][y]='u';
        if(x+1<n){
            if(f[x+1][y]=='*')
                ++pos;
            if(f[x+1][y]=='.')
                dfs(x+1,y,f,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='*')
                ++pos;
            if(f[x-1][y]=='.')
                dfs(x-1,y,f,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='*')
                ++pos;
            if(f[x][y+1]=='.')
                dfs(x,y+1,f,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='*')
                ++pos;
            if(f[x][y-1]=='.')
                dfs(x,y-1,f,n,m);
        }
    }
    static void fill(int x,int y,char f[][],int dp[][],int n,int m){
        dp[x][y]=pos;
        f[x][y]='*';
           if(x+1<n){
            if(f[x+1][y]=='u')
                fill(x+1,y,f,dp,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='u')
                fill(x-1,y,f,dp,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='u')
                fill(x,y+1,f,dp,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='u')
                fill(x,y-1,f,dp,n,m);
        }
    }
    static boolean check(String s){
        int i=0,j=s.length()-1;
        while(i<j){
            if(s.charAt(i)!=s.charAt(j))
                return false;
            ++i;
            --j;
        }
        return true;
    }
    static void update(int s,int e,int l,int r,int in,int v){
        if(s>e||s>r||l>e)
            return;
        if(s>=l&&e<=r){
            seg[in]=v;
            return;
        }
        int mid=(s+e)/2;
        update(s,mid,l,r,2*in+1,v);
        update(mid+1,e,l,r,2*in+2,v);
        seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
        static int query(int s,int e,int l,int r,int in){
        if(s>e||s>r||l>e)
            return 0;
        if(s>=l&&e<=r){
            return seg[in];
            
        }
        int mid=(s+e)/2;
        return Math.max(query(s,mid,l,r,2*in+1),
        query(mid+1,e,l,r,2*in+2));
        //seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
    static double dist(long x,long y,long z,long w){
        return Math.sqrt((x-y)*(x-y)+(z-w)*(z-w));
    }
    static void add(int x,int y,Queue<Integer>q,Queue<Integer>v,int b[][]){
        q.add(x);
        v.add(y);
        b[x][y]=1;
    }
    static long nCr(long n, long r, 
                                    long p) 
    { 
        return (fac[(int)n]* modInverse(fac[(int)r], p) 
                % p * modInverse(fac[(int)(n-r)], p) 
                                    % p) % p; 
    } 
    //static int prime[];
    //static int dp[];
    public static void main(String[] args){
        //long sum=0;
        try {
                codeforces.solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
    }
       static long modInverse(long n, long p) 
    { 
        return power(n, p-(long)2,p); 
    } 
 static long power(long x, long y, long p) 
{ 
    long res = 1;      // Initialize result 
  
    x = x % p;  // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y %(long)2!=0) 
            res = (res*x) % p; 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x) % p;   
    } 
    return res%p;
 }
    /*public static long power(long x,long a) {
		if(a==0) return 1;
		if(a%2==1)return (x*1L*power(x,a-1))%mod;
		return (power((int)((x*1L*x)%mod),a/2))%mod;
	}*/
   static int find(int x) 
    { 
        // Finds the representative of the set 
        // that x is an element of 
        while(parent[x]!=x) 
        { 
            // if x is not the parent of itself 
            // Then x is not the representative of 
            // his set,
            x=parent[x];
  
            // so we recursively call Find on its parent 
            // and move i's node directly under the 
            // representative of this set 
        } 
  
        return x; 
    }
    static void union(int x, int y) 
    { 
        // Find representatives of two sets 
        int xRoot = find(x), yRoot = find(y); 
  
        // Elements are in the same set, no need 
        // to unite anything. 
        if (xRoot == yRoot) 
            return; 
  
         // If x's rank is less than y's rank 
        if (rank[xRoot] < rank[yRoot]) 
  
            // Then move x under y  so that depth 
            // of tree remains less 
            parent[xRoot] = yRoot; 
  
        // Else if y's rank is less than x's rank 
        else if (rank[yRoot] < rank[xRoot]) 
  
            // Then move y under x so that depth of 
            // tree remains less 
            parent[yRoot] = xRoot; 
  
        else // if ranks are the same 
        { 
            // Then move y under x (doesn't matter 
            // which one goes where) 
            parent[yRoot] = xRoot; 
  
            // And increment the the result tree's 
            // rank by 1 
            rank[xRoot] = rank[xRoot] + 1; 
        } 
    } 
    static long gcd(long a, long b) 
    { 
        if (a == 0){ 
             //ans+=b;
            return b;
        }
        return gcd(b % a, a); 
    }
}