There is a binary string a of length n. In one operation, you can select any prefix of a with an equal number of 0 and 1 symbols. Then all symbols in the prefix are inverted: each 0 becomes 1 and each 1 becomes 0.

For example, suppose a=0111010000. 

  * In the first operation, we can select the prefix of length 8 since it has four 0's and four 1's: [01110100]00→ [10001011]00. 
  * In the second operation, we can select the prefix of length 2 since it has one 0 and one 1: [10]00101100→ [01]00101100. 
  * It is illegal to select the prefix of length 4 for the third operation, because it has three 0's and one 1. 



Can you transform the string a into the string b using some finite number of operations (possibly, none)?

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 3⋅ 10^5) — the length of the strings a and b.

The following two lines contain strings a and b of length n, consisting of symbols 0 and 1.

The sum of n across all test cases does not exceed 3⋅ 10^5.

Output

For each test case, output "YES" if it is possible to transform a into b, or "NO" if it is impossible. You can print each letter in any case (upper or lower).

Example

Input


5
10
0111010000
0100101100
4
0000
0000
3
001
000
12
010101010101
100110011010
6
000111
110100


Output


YES
YES
NO
YES
NO

Note

The first test case is shown in the statement.

In the second test case, we transform a into b by using zero operations.

In the third test case, there is no legal operation, so it is impossible to transform a into b.

In the fourth test case, here is one such transformation: 

  * Select the length 2 prefix to get 100101010101. 
  * Select the length 12 prefix to get 011010101010. 
  * Select the length 8 prefix to get 100101011010. 
  * Select the length 4 prefix to get 011001011010. 
  * Select the length 6 prefix to get 100110011010. 



In the fifth test case, the only legal operation is to transform a into 111000. From there, the only legal operation is to return to the string we started with, so we cannot transform a into b.
/*
 * Date Created : 3/4/2021
 * Have A Good Day !
 */

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author arpit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BFlipTheBits solver = new BFlipTheBits();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }
    
    static class BFlipTheBits {
        public void solve(int testNumber, FastReader r, OutputWriter out) {
            int n = r.nextInt();
            char[] a = r.next().toCharArray();
            char[] b = r.next().toCharArray();
            int[] z_cnt = new int[n], o_cnt = new int[n];
            for (int i = 0; i < n; i++) {
                if (i == 0) {
                    if (a[i] == '0') z_cnt[0] = 1;
                    else o_cnt[0] = 1;
                } else {
                    z_cnt[i] = z_cnt[i - 1];
                    o_cnt[i] = o_cnt[i - 1];
                    if (a[i] == '0') z_cnt[i] += 1;
                    else o_cnt[i] += 1;
                }
            }
            boolean flag = true;
            int times_flipped = 0;
            for (int i = n - 1; i >= 0; i--) {
                char curr = a[i];
                if ((times_flipped & 1) != 0) {
                    if (curr == '0') curr = '1';
                    else curr = '0';
                }
                if (curr != b[i]) {
                    if (z_cnt[i] != o_cnt[i]) {
                        flag = false;
                        break;
                    } else {
                        times_flipped++;
                    }
                }
            }
            out.println(flag ? "YES" : "NO");
        }
        
    }
    
    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;
        
        public FastReader(InputStream stream) {
            this.stream = stream;
        }
        
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
        
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        
        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        
        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }
        
        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        
        public String next() {
            return nextString();
        }
        
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
            
        }
        
    }
    
    static class OutputWriter {
        private final PrintWriter writer;
        
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
        
        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                writer.print(objects[i]);
                if (i != objects.length - 1) writer.print(" ");
            }
        }
        
        public void println(Object... objects) {
            print(objects);
            writer.println();
        }
        
        public void close() {
            writer.close();
        }
        
    }
}

