There are n candles on a Hanukkah menorah, and some of its candles are initially lit. We can describe which candles are lit with a binary string s, where the i-th candle is lit if and only if s_i=1.

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Initially, the candle lights are described by a string a. In an operation, you select a candle that is currently lit. By doing so, the candle you selected will remain lit, and every other candle will change (if it was lit, it will become unlit and if it was unlit, it will become lit).

You would like to make the candles look the same as string b. Your task is to determine if it is possible, and if it is, find the minimum number of operations required.

Input

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

The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of candles.

The second line contains a string a of length n consisting of symbols 0 and 1 — the initial pattern of lights.

The third line contains a string b of length n consisting of symbols 0 and 1 — the desired pattern of lights.

It is guaranteed that the sum of n does not exceed 10^5.

Output

For each test case, output the minimum number of operations required to transform a to b, or -1 if it's impossible.

Example

Input


5
5
11010
11010
2
01
11
3
000
101
9
100010111
101101100
9
001011011
011010101


Output


0
1
-1
3
4

Note

In the first test case, the two strings are already equal, so we don't have to perform any operations.

In the second test case, we can perform a single operation selecting the second candle to transform 01 into 11.

In the third test case, it's impossible to perform any operations because there are no lit candles to select.

In the fourth test case, we can perform the following operations to transform a into b: 

  1. Select the 7-th candle: 100010{\color{red}1}11→ 011101{\color{red} 1}00. 
  2. Select the 2-nd candle: 0{\color{red} 1}1101100→ 1{\color{red} 1}0010011. 
  3. Select the 1-st candle: {\color{red}1}10010011→ {\color{red}1}01101100. 



In the fifth test case, we can perform the following operations to transform a into b: 

  1. Select the 6-th candle: 00101{\color{red}1}011→ 11010{\color{red}1}100 
  2. Select the 2-nd candle: 1{\color{red}1}0101100→ 0{\color{red}1}1010011 
  3. Select the 8-th candle: 0110100{\color{red}1}1→ 1001011{\color{red}1}0 
  4. Select the 7-th candle: 100101{\color{red}1}10→ 011010{\color{red}1}01 
import java.util.*;
import java.io.*;

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run() {
        boolean tc = true;
        //AdityaFastIO r = new AdityaFastIO();
        FastReader r = new FastReader();

        try (OutputStream out = new BufferedOutputStream(System.out)) {

            //long startTime = System.currentTimeMillis();

            int testcases = tc ? r.ni() : 1;
            int tcCounter = 1;
            // Hold Here Sparky------------------->>>
            // Solution Starts Here

            start:
            while (testcases-- > 0) {

                int n = r.ni();
                char[] s1 = r.word().toCharArray();
                char[] s2 = r.word().toCharArray();

                int first0 = 0;
                int first1 = 0;
                int second0 = 0;
                int second1 = 0;

                int i = 0;
                while (i < n) {
                    if (s1[i] == '0' && s2[i] == '0') first0++;
                    if (s1[i] == '0' && s2[i] == '1') first1++;
                    if (s1[i] == '1' && s2[i] == '0') second0++;
                    if (s1[i] == '1' && s2[i] == '1') second1++;
                    i++;
                }

                long get = Long.MAX_VALUE;
                long max = Math.max(first0, second1);
                if (first0 + 1 == second1) get = Math.min(get, max * 2L - 1);
                if (first1 == second0) get = Math.min(get, first1 * 2L);
                if (get == Long.MAX_VALUE) get = -1L;

                out.write((get + " ").getBytes());
                out.write(("\n").getBytes());

            }
            // Solution Ends Here
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    static class AdityaFastIO {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

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

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

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

        public String line() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() 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 nl() 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 nd() 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();
        }
    }

    public static void main(String[] args) throws Exception {
        run();
    }

    static long mod = 998244353;

    static long modInv(long base, long e) {
        long result = 1;
        base %= mod;
        while (e > 0) {
            if ((e & 1) > 0) result = result * base % mod;
            base = base * base % mod;
            e >>= 1;
        }
        return result;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

        String line() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int ni() {
            return Integer.parseInt(word());
        }

        long nl() {
            return Long.parseLong(word());
        }

        double nd() {
            return Double.parseDouble(word());
        }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1) result = result * x % MOD;
            n = n / 2;
            x = x * x % MOD;
        }
        return result;
    }

    static long powerStrings(int i1, int i2) {
        String sa = String.valueOf(i1);
        String sb = String.valueOf(i2);
        long a = 0, b = 0;
        for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
        for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
        return powerLL(a, b);
    }

    static long gcd(long a, long b) {
        if (a == 0) return b;
        else return gcd(b % a, a);
    }

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

    static long lower_bound(int[] arr, int x) {
        int l = -1, r = arr.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (arr[m] >= x) r = m;
            else l = m;
        }
        return r;
    }

    static int upper_bound(int[] arr, int x) {
        int l = -1, r = arr.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (arr[m] <= x) l = m;
            else r = m;
        }
        return l + 1;
    }

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
        graph.get(edge1).add(edge2);
        graph.get(edge2).add(edge1);
    }

    public static class Pair implements Comparable<Pair> {
        int first;
        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if (this.first != o.first)
                return (int) (this.first - o.first);
            else return (int) (this.second - o.second);
        }
    }

    public static class PairC<X, Y> implements Comparable<PairC> {
        X first;
        Y second;

        public PairC(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
        return true;
    }

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
        return true;
    }

}