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.
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;

import javax.management.Query;

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

public class Main {
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    } else {
                        continue;
                    }
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    static int arr[];

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int testcase = sc.nextInt();
        while (testcase-- > 0) {
            String x = sc.next();
            String str = sc.next();
            String str1 = sc.next();
            solve(str, str1);
            // System.out.println(solve(str, k));
        }
    }

    public static void solve(String str1, String str2) {
        int arr1_0[] = new int[str1.length()];
        int arr1_1[] = new int[str1.length()];
        int arr2_0[] = new int[str1.length()];
        int arr2_1[] = new int[str1.length()];
        if (str1.charAt(0) == '0')
            arr1_0[0] = 1;
        else
            arr1_1[0] = 1;
        if (str2.charAt(0) == '0')
            arr2_0[0] = 1;
        else
            arr2_1[0] = 1;
        for (int i = 1; i < str1.length(); i++) {
            if (str1.charAt(i) == '0') {
                arr1_0[i] = arr1_0[i - 1] + 1;
                arr1_1[i] = arr1_1[i - 1];
            } else {
                arr1_0[i] = arr1_0[i - 1];
                arr1_1[i] = arr1_1[i - 1] + 1;
            }
        }
        for (int i = 1; i < str2.length(); i++) {
            if (str2.charAt(i) == '0') {
                arr2_0[i] = arr2_0[i - 1] + 1;
                arr2_1[i] = arr2_1[i - 1];
            } else {
                arr2_0[i] = arr2_0[i - 1];
                arr2_1[i] = arr2_1[i - 1] + 1;
            }
        }
        boolean check = false;
        for (int i = arr1_0.length - 1; i >= 0; i--) {
            if (arr1_0[i] == arr1_1[i]) {
                if ((arr1_0[i - 1] == arr2_1[i - 1] && (arr1_1[i - 1] == arr2_0[i - 1])))
                    check = true;
                else
                    check = false;

            } else if (check) {
                int copy = arr1_0[i];
                arr1_0[i] = arr1_1[i];
                arr1_1[i] = copy;
            }

            // System.out.println(arr1_0[i] + " " + arr1_1[i]);
            // System.out.println(arr2_0[i] + " " + arr2_1[i]);
            if (arr1_0[i] != arr2_0[i] || (arr1_1[i] != arr2_1[i])) {
                System.out.println("NO");
                return;
            }
        }
        System.out.println("YES");
    }
    // public static void solve(String s) {
    // boolean check = true;
    // StringBuilder str = new StringBuilder();
    // str.append(s);
    // for (int i = 0; i < str.length(); i++) {
    // if (str.charAt(i) != 'a') {
    // check = false;
    // break;
    // }
    // }
    // if (check) {
    // System.out.println("NO");
    // } else {
    // // int first=0;
    // // int end=s.length()-1;
    // String copy1 = s + "a";
    // System.out.println("YES");
    // if (!isPalindrome(copy1.toCharArray())) {
    // System.out.println(copy1);
    // } else
    // System.out.println("a" + s);
    // // while()
    // }
    // }

    // public static boolean isPalindrome(char[] word) {
    // int start = 0;
    // int end = word.length - 1;
    // while (end > start) {
    // if (word[start] != word[end]) {
    // return false;
    // }
    // ++start;
    // --end;
    // }
    // return true;
    // }
}
// public static void solve(String s) {
// boolean check=palin(s);
// StringBuilder str=new StringBuilder();
// str.append(s);
// if(check&&str.length()%2==0)
// {
// System.out.println("YES");
// str.append("a");
// System.out.println(str);
// }else if()
// }

// }