Problem: Let's denote the following function f. This function takes an array a of length n and returns an array. Initially the result is an empty array. For each integer i from 1 to n we add element a_i to the end of the resulting array if it is greater than all previous elements (more formally, if a_i > max_{1 ≤ j < i}a_j). Some examples of the function f:

  1. if a = [3, 1, 2, 7, 7, 3, 6, 7, 8] then f(a) = [3, 7, 8]; 
  2. if a = [1] then f(a) = [1]; 
  3. if a = [4, 1, 1, 2, 3] then f(a) = [4]; 
  4. if a = [1, 3, 1, 2, 6, 8, 7, 7, 4, 11, 10] then f(a) = [1, 3, 6, 8, 11]. 



You are given two arrays: array a_1, a_2, ... , a_n and array b_1, b_2, ... , b_m. You can delete some elements of array a (possibly zero). To delete the element a_i, you have to pay p_i coins (the value of p_i can be negative, then you get |p_i| coins, if you delete this element). Calculate the minimum number of coins (possibly negative) you have to spend for fulfilling equality f(a) = b.

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of array a.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the array a.

The third line contains n integers p_1, p_2, ..., p_n (|p_i| ≤ 10^9) — the array p.

The fourth line contains one integer m (1 ≤ m ≤ n) — the length of array b.

The fifth line contains m integers b_1, b_2, ..., b_m (1 ≤ b_i ≤ n, b_{i-1} < b_i) — the array b.

Output

If the answer exists, in the first line print YES. In the second line, print the minimum number of coins you have to spend for fulfilling equality f(a) = b.

Otherwise in only line print NO.

Examples

Input


11
4 1 3 3 7 8 7 9 10 7 11
3 5 0 -2 5 3 6 7 8 2 4
3
3 7 10


Output


YES
20


Input


6
2 1 5 3 6 5
3 -9 0 16 22 -14
4
2 3 5 6


Output


NO

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class F {
	
	static long oo=(long)1e18;
	
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int n=fs.nextInt();
		int[] a=fs.readArray(n);
		int[] deleteCost=fs.readArray(n);
		n++;
		int lisLen=fs.nextInt();
		int[] lis=fs.readArray(lisLen);
		lisLen++;
		int lisIndex=0;
		for (int i:a) {
			if (lisIndex<lisLen && lis[lisIndex]==i) lisIndex++;
		}
		if (lisIndex!=lisLen) {
			System.out.println("NO");
			return;
		}
		System.out.println("YES");
		Entry[] allEntries=new Entry[n];
		for (int i=0; i<n; i++) allEntries[i]=new Entry(i, a[i]);
		Arrays.sort(allEntries);
		ArrayList<Integer>[] indeciesOf=new ArrayList[n+1];
		for (int i=0; i<=n; i++) indeciesOf[i]=new ArrayList<>();
		for (int i=0; i<n; i++) indeciesOf[a[i]].add(i);
		BIT bit=new BIT(n);
		for (int i=0; i<n; i++)
			if (deleteCost[i]<0) bit.update(i, deleteCost[i]);
		
		long[] dp=new long[n];
		Arrays.fill(dp, oo);
		int indexInAllEntries=n-1;
		
		for (lisIndex=lisLen-1; lisIndex>=0; lisIndex--) {
			int lisValue=lis[lisIndex];
			while (indexInAllEntries>0 && allEntries[indexInAllEntries].value>lisValue) {
				//we need to pay for it, so add it to the bit if its cost is positive
				int ind=allEntries[indexInAllEntries].index;
				if (deleteCost[ind]>0) bit.update(ind, deleteCost[ind]);
				indexInAllEntries--;
			}
			if (lisIndex==lisLen-1) {
				for (int i:indeciesOf[lisValue]) {
					dp[i]=bit.rangeSum(i+1, n-1);
//					System.out.println("Index "+i+" is "+dp[i]);
				}
			}
			else {
				//we can choose from any of the above dp states
				int bestIndex=-1;
				int nextLisValue=lis[lisIndex+1];
				int candNextIndex=indeciesOf[nextLisValue].size()-1;
				for (int i=indeciesOf[lisValue].size()-1; i>=0; i--) {
					int curIndex=indeciesOf[lisValue].get(i);
					while (candNextIndex>=0) {
						int candIndex=indeciesOf[nextLisValue].get(candNextIndex);
						if (candIndex<curIndex) break;
						if (bestIndex==-1) {
							bestIndex=candIndex;
						}
						else {
							long bestIndexCost=dp[bestIndex]+bit.rangeSum(curIndex+1, bestIndex-1);
							long candIndexCost=dp[candIndex]+bit.rangeSum(curIndex+1, candIndex-1);
							if (bestIndexCost>candIndexCost)
								bestIndex=candIndex;
						}
						candNextIndex--;
					}
					if (bestIndex==-1) {
//						System.out.println("No followup for index: "+curIndex);
						dp[curIndex]=oo;
					}
					else {
//						System.out.println("BestIndex for "+curIndex+" is "+bestIndex);
						dp[curIndex]=dp[bestIndex]+bit.rangeSum(curIndex+1, bestIndex-1);
					}
				}
			}
		}
		
		long ans=oo;
		for (int i=0; i<n; i++)
			if (a[i]==lis[0]) ans=Math.min(ans, dp[i]);
		System.out.println(ans);
//		System.out.println(Arrays.toString(dp));
	}
	
	static class Entry implements Comparable<Entry> {
		int index, value;
		public Entry(int index, int value) {
			this.index=index;
			this.value=value;
		}
		
		public int compareTo(Entry o) {
			return Integer.compare(value, o.value);
		}
	}
	
	static class BIT {
		int n;
		long[] tree;
		
		public BIT(int n) {
			this.n = n;
			tree = new long[n + 2];
		}
		
		long read(int i) {
			i++;
			long sum = 0;
			while (i > 0) {
				sum += tree[i];
				i -= i & -i;
			}
			return sum;
		}
		
		void update(int i, long val) {
			i++;
			while (i <= n) {
				tree[i] += val;
				i += i & -i;
			}
		}
		
		long rangeSum(int from, int to) {
			if (from==0) return read(to);
			return read(to)-read(from-1);
		}
		
		// if the BIT is a freq array, returns the
		// index of the kth item, or n if there are fewer
		// than k items.
		int getKth(int k) {
			int e=Integer.highestOneBit(n), o=0;
			for (; e!=0; e>>=1) {
				if (e+o<=n && tree[e+o]<=k) {
					k-=tree[e+o];
					o+=e;
				}
			}
			return o;
		}
		
	}

	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");

		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int[] readArray(int n) {
			int[] a=new int[n+1];
			for (int i=0; i<n; i++) {
				a[i+1]=nextInt();
			}
			return a;
		}

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

	}
	
}