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.
3
1 2 4
2 2 1
 5
5 4 2 6 10
2 4 3 3 2
 4
2 1 2 2
2 3 3 2
 8
1 2 2 9 7 5 6 5
8 4 1 5 5 1 1 8
 3
76 74 84
3 2 1
 3
1 2 4
2 3 3
 7
2 1 64 8 32 4 16
5 7 2 4 2 4 6
 3
1 2 4
3 2 3
 5
1 1 10 10 10
2 3 4 5 3
 4
1 12 2 3
2 3 4 2
 4
99 71 47 82
1 3 4 2
 5
1 2 3 4 5
3 4 5 3 2
 4
90 5 66 84
3 1 2 4
 3
9 5 6
3 3 1
 8
8 8 1 10 6 9 3 1
5 2 7 1 6 8 4 3
 3
80 6 67
1 2 3
 10
10 10 10 10 1 10 10 10 10 10
2 3 4 5 3 2 6 9 5 8
 10
6870 3547 3337 9426 3866 1873 4908 4628 7800 6716
2 3 4 5 1 4 6 2 8 9
 4
97 27 70 99
1 2 3 4
 4
2 58 52 89
3 1 4 2
 3
1 2 4
1 3 1
 3
1 2 4
3 3 3
 4
81 69 80 19
4 3 1 2
 4
4 95 20 62
2 1 4 3
 2
62 49
1 2
 4
1 2 4 8
2 3 3 2
 8
1 8 32 4 16 64 128 2
6 4 1 5 4 4 1 3
 2
21 28
2 1
 10
5620 2478 4051 7060 6327 2170 6912 2031 1781 7454
1 1 1 1 1 1 1 1 1 1
 6
10 7 1 1 8 2
5 5 2 3 3 5
 2
1 2
2 2
 10
6 9 1 1 1 10 2 4 9 6
5 3 4 2 6 8 9 1 10 7
 3
15 52 14
1 3 2
 1
12
1
 5
1 16 2 4 8
5 3 1 5 4
 4
88 78 39 46
4 3 2 1
 3
1 2 4
3 3 1
 3
1 2 4
3 2 2
 4
37 86 1 88
4 2 1 3
 10
6724 5003 9029 376 7529 5554 1407 388 2632 981
2 3 4 5 1 4 6 7 8 9
 10
1337 4359 5138 5246 7859 8111 1154 8455 3711 1737
1 1 2 3 4 1 6 7 8 9
 3
40 26 88
3 1 2
 10
7846 8354 1188 6898 8046 7561 8043 8588 8684 3699
1 1 2 3 4 5 6 7 8 9
 7
4 32 8 1 16 64 2
6 1 5 2 1 4 5
 3
30 98 37
2 3 1
 3
17 34 88
2 1 3
 10
9 19 19 1 3 9 1 12 10 8
7 1 6 3 4 8 5 10 2 9

2 2 2 12 150 4 8 6 10 2 146 2 89 6 9 153 1 3337 293 2 1 4 19 24 111 4 4 21 5620 1 2 4 29 12 4 85 1 2 87 376 1337 26 7846 1 30 105 1
import java.io.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
public class Main{
         public static ArrayList a[]=new ArrayList[300001];
         static boolean visited[]=new boolean [300001];
         static long cost[],ans;
         static int cnt[]=new int[300001];
         static int count=0;
         static Stack<Integer>st=new Stack<>();
         static Vector<Integer>topo=new Vector<>();
         static boolean chk;
         static long mini,isNum;
         static void ini() {
        	 st.clear();
        	 chk=false;
        	 isNum=0;
        	 mini=Long.MAX_VALUE;
         }
         static void dfs(int n) {
        	 visited[n]=true;
        	 for(int i=0;i<a[n].size();i++)
        	 {
        		 int id=(int) a[n].get(i);
        		 if(!visited[id]) {
        			 dfs(id);
        		 }
        	 }
        	 topo.add(n);
         }
         static void dfs1(int n) {
        	 cnt[n]=count;
        	 for(int i=0;i<a[n].size();i++)
        	 {
        		 int id=(int) a[n].get(i);
        		 if(cnt[id]==0) {
        			 if(!chk)
        				 st.push(id);
        			 dfs1(id);
        			 
        		 }
        		 else if(cnt[id]==cnt[n] && !chk) {
        			 chk=true;
        			 isNum=id;
        		 }
        	 }
        	
         }
         static void pre() {
        	 if(chk==true) {
        		 while(!st.isEmpty()) {
        			 int ff=st.pop();
        			 mini=Math.min(mini, cost[ff]);
        			 if(ff==isNum)
        				 break;
        		 }
        		 ans+=mini;
        	 }
        		
         }
         public static void main(String[] args) 
        {
            InputReader in = new InputReader(System.in);
            PrintWriter pw = new PrintWriter(System.out);
            int n=in.nextInt();
            cost=new long[n+1];
            for(int i=1;i<=n;i++)
            {
            	cost[i]=in.nextLong();
            	a[i]=new ArrayList<Integer>();
            }
            for(int i=1;i<=n;i++) {
            	int v=in.nextInt();
            	a[i].add(v);
            }
            for(int i=1;i<=n;i++)
            {
            	if(!visited[i])
            		dfs(i);
            }
            for(int i=topo.size()-1;i>=0;i--) {
            	int id=topo.get(i);
            	if(cnt[id]==0) {
            		count++;
            		
            		ini();
            		st.add(id);
            		dfs1(id);
            		pre();
            	}
            }
            pw.println(ans);
            pw.flush();
            pw.close();
        
        
        }
         
		private static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        
        public static int[] suffle(int[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                int temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
       /* public static long primeFactorization(long n)
        {
             HashSet<Integer> a =new HashSet<Integer>();
        	long cnt=0;
            for(int i=2;i*i<=n;i++)
            {
                while(a%i==0)
                {
                    a.add(i);
                    a/=i;
                }
            }
            if(a!=1)
            	cnt++;
                //a.add(n);
            return cnt;
        }*/
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static int GCD(int a,int b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static long GCD(long a,long b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static void extendedEuclid(int A,int B)
        {
            if(B==0)
            {
                d = A;
                p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(B, A%B);
                int temp = p;
                p = q;
                q = temp - (A/B)*q;
            }
        }
        
        public static long LCM(long a,long b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int LCM(int a,int b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static boolean isPrime(int n)
        {
            
            if (n <= 1)  return false;
            if (n <= 3)  return true;
            
            if (n%2 == 0 || n%3 == 0) 
                return false;
         
            for (int i=5; i*i<=n; i=i+6)
            {
                if (n%i == 0 || n%(i+2) == 0)
                   return false;
            }
            
            return true;
        }
        
         public static long[] shuffle(long[] a, Random gen){ 
                for(int i = 0, n = a.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    long d = a[i]; 
                    a[i] = a[ind]; 
                    a[ind] = d; 
                } 
                return a; 
            }
        static class pair implements Comparable<pair>
        {
            Long x;
            Long y;
            pair(long l,long ans)
            {
                this.x=l;
                this.y=ans;
            }
 

 
 
 
 
 
        public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
            return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Long(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
       
 
      
}
class query {
	Long x;
	Integer y,z;
	query(long x,int y,int z){
		this.x=x;
		this.y=y;
		this.z=z;
	}
}