Problem:
Round Table of Sages

$N$ sages are sitting around a round table with $N$ seats. Each sage holds chopsticks with his dominant hand to eat his dinner. The following happens in this situation.

If sage $i$ is right-handed and a left-handed sage sits on his right, a level of frustration $w_i$ occurs to him. A right-handed sage on his right does not cause such frustration at all.

If sage $i$ is left-handed and a right-handed sage sits on his left, a level of frustration $w_i$ occurs to him. A left-handed sage on his left does not cause such frustration at all.

You wish you could minimize the total amount of frustration by clever sitting order arrangement.

Given the number of sages with his dominant hand information, make a program to evaluate the minimum frustration achievable.

Input

The input is given in the following format.

$N$
$a_1$ $a_2$ $...$ $a_N$
$w_1$ $w_2$ $...$ $w_N$

The first line provides the number of sages $N$ ($3 \leq N \leq 10$). The second line provides an array of integers $a_i$ (0 or 1) which indicate if the $i$-th sage is right-handed (0) or left-handed (1). The third line provides an array of integers $w_i$ ($1 \leq w_i \leq 1000$) which indicate the level of frustration the $i$-th sage bears.

Output

Output the minimum total frustration the sages bear.

Sample Input 1

5
1 0 0 1 0
2 3 5 1 2

Sample Output 1

3

Sample Input 2

3
0 0 0
1 2 3

Sample Output 2

0

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main {

	static void solve (FastScanner in, PrintWriter out, Methods ms) {

		int n = in.nextInt();
		int[] a = in.nextIntArray(n);
		int[] b = in.nextIntArray(n);

		Kenja[] kenjas = new Kenja[n];
		for (int i=0; i<n; i++) {
			char c = a[i]==0 ? 'R' : 'L';
			kenjas[i] = new Kenja(c, b[i]);
		}

		ArrayList<Integer> list = new ArrayList<>();
		for (int i=0; i<n; i++) list.add(i);

		int ans = Integer.MAX_VALUE;
		int tail = n-1;
		while (list.size() != 0) {
			int tempSum = 0;
			for (int i=0; i<n; i++) {
				int L = i==0? n-1 : i-1;
				int R = i==n-1? 0 : i+1;
				if ((kenjas[list.get(i)].hand == 'L' && kenjas[list.get(L)].hand == 'R')
						|| (kenjas[list.get(i)].hand == 'R' && kenjas[list.get(R)].hand == 'L')) {
					tempSum += kenjas[list.get(i)].fuman;
				}
			}
			ans = Math.min(ans, tempSum);
			list = nextPermutation(list);
		}

		out.println(ans);

	}

	static class Kenja {
		char hand;
		int fuman;
		Kenja (char hand, int fuman) {
			this.hand = hand;
			this.fuman = fuman;
		}
	}

	static ArrayList<Integer> nextPermutation (ArrayList<Integer> list) {
		int pivotPos = -1;
		int pivot = 0;

		for (int i=list.size()-2; i>=0; i--) {
			if (list.get(i) < list.get(i+1)) {
				pivotPos = i;
				pivot = list.get(i);
				break;
			}
		}

		if (pivotPos==-1 && pivot==0) {
			list.clear();
			return list;
		}

		int L = pivotPos+1, R = list.size()-1;
		int minPos = -1;
		int min = Integer.MAX_VALUE;
		for (int i=R; i>=L; i--) {
			if (pivot < list.get(i)) {
				if (list.get(i) < min) {
					min = list.get(i);
					minPos = i;
				}
			}
		}

		Collections.swap(list, pivotPos, minPos);
		Collections.sort(list.subList(L, R+1));

		return list;

	}



	public static void main (String[] args) {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		Methods ms = new Methods();
		solve(in, out, ms);
		in.close();
		out.close();
	}

	static class Methods {

		public void print (Object... ar) {System.out.println(Arrays.deepToString(ar));}

		public int max (int... ar) {Arrays.sort(ar); return ar[ar.length-1];}

		public int min (int... ar) {Arrays.sort(ar); return ar[0];}

		public long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}

		public long lcm (long a, long b) {return a/gcd(a,b)*b;}

		public long factorial (int i) {
			if (i==1) return 1;
			else return i*factorial(i-1);
		}

		public int manhat (int x1, int y1, int x2, int y2) {
			return Math.abs(x1-x2)+Math.abs(y1-y2);
		}

		public double euclid (double x1, double y1, double x2, double y2) {
			return Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
		}

		public boolean isPrime (int n) {
			if (n==2) return true;
			if (n<2 || n%2==0) return false;
			for (int i=3; i<=Math.sqrt(n); i+=2) if(n%i==0) return false;
			return true;
		}

	}

	static class FastScanner {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private  int length = 0, p = 0;

		public FastScanner (InputStream stream) {
			in = stream;
		}

		public boolean hasNextByte () {
			if (p < length) return true;
			else {
				p = 0;
				try {length = in.read(buffer);}
				catch (Exception e) {e.printStackTrace();}
				if (length <= 0) return false;
			}
			return true;
		}

		public int readByte () {
			if (hasNextByte() == true) return buffer[p++];
			return -1;
		}

		public boolean isPrintable (int n) {return 33<=n&&n<=126;}

		public void skip () {
			while (hasNextByte() && !isPrintable(buffer[p])) p++;
		}

		public boolean hasNext () {skip(); return hasNextByte();}

		public String next () {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int t = readByte();
			while (isPrintable(t)) {
				sb.appendCodePoint(t);
				t = readByte();
			}
			return sb.toString();
		}

		public String[] nextArray (int n) {
			String[] ar = new String[n];
			for (int i=0; i<n; i++) ar[i] = next();
			return ar;
		}

		public int nextInt () {return Math.toIntExact(nextLong());}

		public int[] nextIntArray (int n) {
			int[] ar = new int[n];
			for (int i=0; i<n; i++) ar[i] = nextInt();
			return ar;
		}

		public long nextLong () {
			if (!hasNext()) throw new NoSuchElementException();
			boolean minus = false;
			int temp = readByte();
			if (temp == '-') {
				minus = true;
				temp = readByte();
			}
			if (temp<'0' || '9'<temp) throw new NumberFormatException();
			long n = 0;
			while (isPrintable(temp)) {
				if ('0'<=temp && temp<='9') {
					n *= 10;
					n += temp - '0';
				}
				else throw new NumberFormatException();
				temp = readByte();
			}
			return minus? -n : n;
		}

		public long[] nextLongArray (int n) {
			long[] ar = new long[n];
			for (int i=0; i<n; i++) ar[i] = nextLong();
			return ar;
		}

		public double nextDouble () {
			return Double.parseDouble(next());
		}

		public double[] nextDoubleArray (int n) {
			double[] ar = new double[n];
			for (int i=0; i<n; i++) ar[i] = nextDouble();
			return ar;
		}

		public void close () {
			try {in.close();}
			catch(Exception e){}
		}

	}

}