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.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.math.BigDecimal;
    import java.math.RoundingMode;
    import java.util.*;

    import javax.lang.model.type.IntersectionType;
    import javax.swing.text.html.CSS;
    public class codeforces {
        public static boolean isPalindrome(String str){
            StringBuilder sb=new StringBuilder(str);
            sb.reverse();
            String rev=sb.toString();
            if(str.equals(rev)){
                return true;
            }else{
                return false;
            }
        }
        public static void main(String[] args) {
            PrintWriter out = new PrintWriter(System.out);
            InputReader sc = new InputReader(System.in);
                int t=sc.nextInt();
            while(t-->0) {
                int n=sc.nextInt();
                String x=sc.next();
                String y=sc.next();
                int flag=0;
                String temp="";
                int zero=0,one=0;
                String x1="";
                StringBuilder s=new StringBuilder();
                ArrayList<Integer> al=new ArrayList<>();
                for(int i=0;i<n;i++)
                {
                    if(x.charAt(i)=='0') {
                        s.append("1");
                        zero++;
                    }
                    else {
                        one++;
                        s.append("0");
                    }
                    if(zero==one)
                        al.add(i);
                }
                x1=s.toString();
                if(x.equals(y))
                    System.out.println("YES");
                else {
                    if (al.size() == 0)
                        System.out.println("NO");
                    else {
                        if (al.get(al.size() - 1) == n - 1) {
                            for (int i = al.size() - 1; i>= 0; i--) {
                                if((i-1)>=0) {
                                    String a= x.substring(al.get(i - 1) + 1, al.get(i) + 1);
                                    if(a.equals(y.substring(al.get(i - 1) + 1, al.get(i) + 1)))
                                        continue;
                                    a=x1.substring(al.get(i - 1) + 1, al.get(i) + 1);
                                    if (a.equals(y.substring(al.get(i - 1) + 1, al.get(i) + 1))) {
                                        temp = x;
                                        x = x1;
                                        x1 = temp;
                                    }
                                    else {
                                        flag = 1;
                                        break;
                                    }
                                }
                                else
                                {
                                    String a= x.substring(0, al.get(i) + 1);
                                    if(a.equals(y.substring(0, al.get(i) + 1)))
                                        continue;
                                    a=x1.substring(0, al.get(i) + 1);
                                    if (a.equals(y.substring(0, al.get(i) + 1))) {
                                        temp = x;
                                        x = x1;
                                        x1 = temp;
                                    }
                                    else {
                                        flag = 1;
                                        break;
                                    }
                                }
                            }
                            if (flag == 0) {
                                System.out.println("YES");
                            } else
                                System.out.println("NO");
                        }
                        else
                        {
                            if(al.get(al.size() - 1) != n - 1) {
                                if(!(x.substring(al.get(al.size()-1)+1).equals(y.substring(al.get(al.size()-1)+1))))
                                    System.out.println("NO");
                                else
                                {
                                    for (int i = al.size() - 1; i>= 0; i--) {
                                        if((i-1)>=0) {

                                            String a= x.substring(al.get(i - 1) + 1, al.get(i) + 1);
                                            if(a.equals(y.substring(al.get(i - 1) + 1, al.get(i) + 1)))
                                                continue;
                                            a=x1.substring(al.get(i - 1) + 1, al.get(i) + 1);
                                            if (a.equals(y.substring(al.get(i - 1) + 1, al.get(i) + 1))) {
                                                temp = x;
                                                x = x1;
                                                x1 = temp;
                                            }
                                            else {
                                                flag = 1;
                                                break;
                                            }
                                        }
                                        else
                                        {
                                            String a= x.substring(0, al.get(i) + 1);
                                            if(a.equals(y.substring(0, al.get(i) + 1)))
                                                continue;
                                            a=x1.substring(0, al.get(i) + 1);
                                            if (a.equals(y.substring(0, al.get(i) + 1))) {
                                                temp = x;
                                                x = x1;
                                                x1 = temp;
                                            }
                                            else {
                                                flag = 1;
                                                break;
                                            }
                                        }
                                    }
                                    if (flag == 0) {
                                        System.out.println("YES");
                                    } else
                                        System.out.println("NO");
                                }

                            }
                        }
                    }

                }
            }
        }





        static class InputReader {
            private InputStream in;
            private byte[] buffer = new byte[1024];
            private int curbuf;
            private int lenbuf;
            public InputReader(InputStream in) {
                this.in = in;
                this.curbuf = this.lenbuf = 0;
            }
            public boolean hasNextByte() {
                if (curbuf >= lenbuf) {
                    curbuf = 0;
                    try {
                        lenbuf = in.read(buffer);
                    } catch (IOException e) {
                        throw new InputMismatchException();
                    }
                    if (lenbuf <= 0)
                        return false;
                }
                return true;
            }

            private int readByte() {
                if (hasNextByte())
                    return buffer[curbuf++];
                else
                    return -1;
            }

            private boolean isSpaceChar(int c) {
                return !(c >= 33 && c <= 126);
            }

            private void skip() {
                while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                    curbuf++;
            }

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

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

            public int nextInt() {
                if (!hasNext())
                    throw new NoSuchElementException();
                int c = readByte();
                while (isSpaceChar(c))
                    c = readByte();
                boolean minus = false;
                if (c == '-') {
                    minus = true;
                    c = readByte();
                }
                int res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res = res * 10 + c - '0';
                    c = readByte();
                } while (!isSpaceChar(c));
                return (minus) ? -res : res;
            }

            public long nextLong() {
                if (!hasNext())
                    throw new NoSuchElementException();
                int c = readByte();
                while (isSpaceChar(c))
                    c = readByte();
                boolean minus = false;
                if (c == '-') {
                    minus = true;
                    c = readByte();
                }
                long res = 0;
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res = res * 10 + c - '0';
                    c = readByte();
                } while (!isSpaceChar(c));
                return (minus) ? -res : res;
            }

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

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

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

            public char[][] nextCharMap(int n, int m) {
                char[][] map = new char[n][m];
                for (int i = 0; i < n; i++)
                    map[i] = next().toCharArray();
                return map;
            }
        }
    }
    class SegTree<S> {
        final int MAX;

        final int N;
        final java.util.function.BinaryOperator<S> op;
        final S E;

        final S[] data;

        @SuppressWarnings("unchecked")
        public SegTree(int n, java.util.function.BinaryOperator<S> op, S e) {
            this.MAX = n;
            int k = 1;
            while (k < n) k <<= 1;
            this.N = k;
            this.E = e;
            this.op = op;
            this.data = (S[]) new Object[N << 1];
            java.util.Arrays.fill(data, E);
        }

        public SegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e) {
            this(dat.length, op, e);
            build(dat);
        }

        private void build(S[] dat) {
            int l = dat.length;
            System.arraycopy(dat, 0, data, N, l);
            for (int i = N - 1; i > 0; i--) {
                data[i] = op.apply(data[i << 1 | 0], data[i << 1 | 1]);
            }
        }

        public void set(int p, S x) {
            exclusiveRangeCheck(p);
            data[p += N] = x;
            p >>= 1;
            while (p > 0) {
                data[p] = op.apply(data[p << 1 | 0], data[p << 1 | 1]);
                p >>= 1;
            }
        }

        public S get(int p) {
            exclusiveRangeCheck(p);
            return data[p + N];
        }

        public S prod(int l, int r) {
            if (l > r) {
                throw new IllegalArgumentException(
                        String.format("Invalid range: [%d, %d)", l, r)
                );
            }
            inclusiveRangeCheck(l);
            inclusiveRangeCheck(r);
            S sumLeft = E;
            S sumRight = E;
            l += N; r += N;
            while (l < r) {
                if ((l & 1) == 1) sumLeft = op.apply(sumLeft, data[l++]);
                if ((r & 1) == 1) sumRight = op.apply(data[--r], sumRight);
                l >>= 1; r >>= 1;
            }
            return op.apply(sumLeft, sumRight);
        }

        public S allProd() {
            return data[1];
        }

        public int maxRight(int l, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(l);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (l == MAX) return MAX;
            l += N;
            S sum = E;
            do {
                l >>= Integer.numberOfTrailingZeros(l);
                if (!f.test(op.apply(sum, data[l]))) {
                    while (l < N) {
                        l = l << 1;
                        if (f.test(op.apply(sum, data[l]))) {
                            sum = op.apply(sum, data[l]);
                            l++;
                        }
                    }
                    return l - N;
                }
                sum = op.apply(sum, data[l]);
                l++;
            } while ((l & -l) != l);
            return MAX;
        }

        public int minLeft(int r, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(r);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (r == 0) return 0;
            r += N;
            S sum = E;
            do {
                r--;
                while (r > 1 && (r & 1) == 1) r >>= 1;
                if (!f.test(op.apply(data[r], sum))) {
                    while (r < N) {
                        r = r << 1 | 1;
                        if (f.test(op.apply(data[r], sum))) {
                            sum = op.apply(data[r], sum);
                            r--;
                        }
                    }
                    return r + 1 - N;
                }
                sum = op.apply(data[r], sum);
            } while ((r & -r) != r);
            return 0;
        }

        private void exclusiveRangeCheck(int p) {
            if (p < 0 || p >= MAX) {
                throw new IndexOutOfBoundsException(
                        String.format("Index %d out of bounds for the range [%d, %d).", p, 0, MAX)
                );
            }
        }

        private void inclusiveRangeCheck(int p) {
            if (p < 0 || p > MAX) {
                throw new IndexOutOfBoundsException(
                        String.format("Index %d out of bounds for the range [%d, %d].", p, 0, MAX)
                );
            }
        }
    }
    class MathLib{
        static int LowerBound(int a[], int x) { // x is the target value or key
            int l=-1,r=a.length;
            while(l+1<r) {
                int m=(l+r)>>>1;
                if(a[m]>=x) r=m;
                else l=m;
            }
            return r;
        }
        static int UpperBound(int a[], int x) {// x is the key or target value
            int l=-1,r=a.length;
            while(l+1<r) {
                int m=(l+r)>>>1;
                if(a[m]<=x) l=m;
                else r=m;
            }
            return l+1;
        }
        private static long safe_mod(long x, long m){
            x %= m;
            if(x<0) x += m;
            return x;
        }

        private static long[] inv_gcd(long a, long b){
            a = safe_mod(a, b);
            if(a==0) return new long[]{b,0};

            long s=b, t=a;
            long m0=0, m1=1;
            while(t>0){
                long u = s/t;
                s -= t*u;
                m0 -= m1*u;
                long tmp = s; s = t; t = tmp;
                tmp = m0; m0 = m1; m1 = tmp;
            }
            if(m0<0) m0 += b/s;
            return new long[]{s,m0};
        }

        public static long gcd(long a, long b){
            a = java.lang.Math.abs(a);
            b = java.lang.Math.abs(b);
            return inv_gcd(a, b)[0];
        }
        public static long lcm(long a, long b){
            a = java.lang.Math.abs(a);
            b = java.lang.Math.abs(b);
            return a / gcd(a,b) * b;
        }

        public static long pow_mod(long x, long n, int m){
            assert n >= 0;
            assert m >= 1;
            if(m == 1)return 0L;
            x = safe_mod(x, m);
            long ans = 1L;
            while(n > 0){
                if((n&1) == 1) ans = (ans * x) % m;
                x = (x*x) % m;
                n >>>= 1;
            }
            return ans;
        }

        public static long[] crt(long[] r, long[] m){
            assert(r.length == m.length);
            int n = r.length;

            long r0=0, m0=1;
            for(int i=0; i<n; i++){
                assert(1 <= m[i]);
                long r1 = safe_mod(r[i], m[i]), m1 = m[i];
                if(m0 < m1){
                    long tmp = r0; r0 = r1; r1 = tmp;
                    tmp = m0; m0 = m1; m1 = tmp;
                }
                if(m0%m1 == 0){
                    if(r0%m1 != r1) return new long[]{0,0};
                    continue;
                }

                long[] ig = inv_gcd(m0, m1);
                long g = ig[0], im = ig[1];

                long u1 = m1/g;
                if((r1-r0)%g != 0) return new long[]{0,0};

                long x = (r1-r0) / g % u1 * im % u1;

                r0 += x * m0;
                m0 *= u1;
                if(r0<0) r0 += m0;
                //System.err.printf("%d %d\n", r0, m0);
            }
            return new long[]{r0, m0};
        }
        public static long floor_sum(long n, long m, long a, long b){
            long ans = 0;
            if(a >= m){
                ans += (n-1) * n * (a/m) / 2;
                a %= m;
            }
            if(b >= m){
                ans += n * (b/m);
                b %= m;
            }

            long y_max = (a*n+b) / m;
            long x_max = y_max * m - b;
            if(y_max == 0) return ans;
            ans += (n - (x_max+a-1)/a) * y_max;
            ans += floor_sum(y_max, a, m, (a-x_max%a)%a);
            return ans;
        }

        public static java.util.ArrayList<Long> divisors(long n){
            java.util.ArrayList<Long> divisors = new ArrayList<>();
            java.util.ArrayList<Long> large = new ArrayList<>();

            for(long i=1; i*i<=n; i++) if(n%i==0){
                divisors.add(i);
                if(i*i<n) large.add(n/i);
            }
            for(int p=large.size()-1; p>=0; p--){
                divisors.add(large.get(p));
            }
            return divisors;
        }
    }
