You are given a permutation p_1, p_2, ... , p_n (an array where each integer from 1 to n appears exactly once). The weight of the i-th element of this permutation is a_i.

At first, you separate your permutation into two non-empty sets — prefix and suffix. More formally, the first set contains elements p_1, p_2, ... , p_k, the second — p_{k+1}, p_{k+2}, ... , p_n, where 1 ≤ k < n.

After that, you may move elements between sets. The operation you are allowed to do is to choose some element of the first set and move it to the second set, or vice versa (move from the second set to the first). You have to pay a_i dollars to move the element p_i.

Your goal is to make it so that each element of the first set is less than each element of the second set. Note that if one of the sets is empty, this condition is met.

For example, if p = [3, 1, 2] and a = [7, 1, 4], then the optimal strategy is: separate p into two parts [3, 1] and [2] and then move the 2-element into first set (it costs 4). And if p = [3, 5, 1, 6, 2, 4], a = [9, 1, 9, 9, 1, 9], then the optimal strategy is: separate p into two parts [3, 5, 1] and [6, 2, 4], and then move the 2-element into first set (it costs 1), and 5-element into second set (it also costs 1).

Calculate the minimum number of dollars you have to spend.

Input

The first line contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of permutation.

The second line contains n integers p_1, p_2, ... , p_n (1 ≤ p_i ≤ n). It's guaranteed that this sequence contains each element from 1 to n exactly once.

The third line contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ 10^9).

Output

Print one integer — the minimum number of dollars you have to spend.

Examples

Input


3
3 1 2
7 1 4


Output


4


Input


4
2 4 1 3
5 9 8 3


Output


3


Input


6
3 5 1 6 2 4
9 1 9 9 1 9


Output


2
//package educational.round81;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] P = na(n);
		for(int i = 0;i < n;i++)P[i]--;
		
		int[] iind = new int[n];
		for(int i = 0;i < n;i++){
			iind[P[i]] = i;
		}
		int[] a = na(n);
		StarrySkyTreeL sst = new StarrySkyTreeL(n+1);
		for(int i = 0;i < n;i++){
			sst.add(i+1, n+1, a[i]);
		}
		
		// 7 1 4  0 7 8 12
		//        0 7 6 10
		long ans = Long.MAX_VALUE;
		ans = Math.min(ans, sst.min(1, n));
		for(int i = 0;i < n;i++){
			int ind = iind[i];
			sst.add(ind+1, n+1, -a[ind]);
			sst.add(0, ind+1, a[ind]);
			ans = Math.min(ans, sst.min(1, n));
		}
		out.println(ans);
	}
	
	public static class StarrySkyTreeL {
		public int M, H, N;
		public long[] st;
		public long[] plus;
		public long I = Long.MAX_VALUE/4; // I+plus<long
		
		public StarrySkyTreeL(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			plus = new long[H];
		}
		
		public StarrySkyTreeL(long[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			plus = new long[H];
			Arrays.fill(st, H+N, M, I);
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			st[i] = Math.min(st[2*i], st[2*i+1]) + plus[i];
		}
		
		public void add(int l, int r, long v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, long v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(cl < r && l < mid){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public long min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private long min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				long ret = I;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public void fall(int i)
		{
			if(i < H){
				if(2*i < H){
					plus[2*i] += plus[i];
					plus[2*i+1] += plus[i];
				}
				st[2*i] += plus[i];
				st[2*i+1] += plus[i];
				plus[i] = 0;
			}
		}
		
		public int firstle(int l, long v) {
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur;
					}else{
						return cur-H;
					}
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}
		
		public int lastle(int l, long v) {
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur+1;
					}else{
						return cur-H;
					}
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}
		
		public void addx(int l, int r, long v){
			if(l >= r)return;
			while(l != 0){
				int f = l&-l;
				if(l+f > r)break;
				if(f == 1){
					st[(H+l)/f] += v;
				}else{
					plus[(H+l)/f] += v;
				}
				l += f;
			}
			
			while(l < r){
				int f = r&-r;
				if(f == 1){
					st[(H+r)/f-1] += v;
				}else{
					plus[(H+r)/f-1] += v;
				}
				r -= f;
			}
		}
		
		public long minx(int l, int r){
			long lmin = I;
			if(l >= r)return lmin;
			if(l != 0){
				for(int d = 0;H>>>d > 0;d++){
					if(d > 0){
						int id = (H+l-1>>>d);
						lmin += plus[id];
					}
					if(l<<~d<0 && l+(1<<d) <= r){
						long v = st[H+l>>>d];
						if(v < lmin)lmin = v;
						l += 1<<d;
					}
				}
			}
			long rmin = I;
			for(int d = 0;H>>>d > 0;d++){
				if(d > 0 && r < H)rmin += plus[H+r>>>d];
				if(r<<~d<0 && l < r){
					long v = st[(H+r>>>d)-1];
					if(v < rmin)rmin = v;
					r -= 1<<d;
				}
			}
			long min = Math.min(lmin, rmin);
			return min;
		}
		
		public long[] toArray() { return toArray(1, 0, H, new long[H]); }
		
		private long[] toArray(int cur, int l, int r, long[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
