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

public class Main {
    
    InputStream is;
    FastWriter out;
    String INPUT = "";

    void run() throws Exception
    {
        is = System.in;
        out = new FastWriter(System.out);
        solve();
        out.flush();
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
 
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }

    private int[] na2(int n)
    {
        int[] a = new int[n+1];
        a[0] = 0;
        for(int i = 1;i <= n;i++)a[i] = ni();
        return a;
    }
 
    private long[] nal(int n)
    {
        long[] a = new long[n];
        for(int i = 0;i < n;i++)a[i] = nl();
        return a;
    }
 
    private long[] nal2(int n)
    {
        long[] a = new long[n+1];
        a[0] = 0L;
        for(int i = 1;i <= n;i++)a[i] = nl();
        return a;
    }
 
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
 
    private int[][] nmi(int n, int m) {
        int[][] map = new int[n][];
        for(int i = 0;i < n;i++)map[i] = na(m);
        return map;
    }
 
    private int ni() { return (int)nl(); }
 
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
 
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private int gcd(int a, int b) {
        if(b == 0)
            return a;
        if(a == 0)
            return b;
        return gcd(b, a%b);
    }

    private int gcdRange(int l, int r) {
        int ans = 1;
        for (int i = r; i >= 1; i--) {
            if ((r / i) - (l - 1) / i > 1) {
                ans = i;
                break;
            }
        }
        return ans;
    }

    // ∑i = gcd(a1,a2,... ,ai) = gcd(a1) + gcd(a1,a2) + gcd(a1,a2,a3) + gcd(a1,a2,a3,a4) + .............;
    private void gcdPrefix(int[] a, int n) {
        int[] f = new int[5000001];
        for(int v : a) f[v]++;
        for(int i = 1;i <= 5000000;i++){
            for(int j = i*2;j <= 5000000;j+=i){
                f[i] += f[j];
            }
        }
        long[] dp = new long[5000001];
        long ans = 0;
        for(int i = 5000000;i >= 1;i--){
            dp[i] = (long)f[i] * i;
            for(int j = i*2;j <= 5000000;j+=i){
                dp[i] = Math.max(dp[i], dp[j] + (long)(f[i] - f[j]) * i);
            }
            ans = Math.max(ans, dp[i]);
        }
        out.println(ans);
    }

    private int findTrailingZerosInFactorial(int n)
    {
    //  5 -> 1 , 10 -> 2 , 20 -> 4 , 100 -> 24
        if (n < 0)
            return -1;
        int count = 0;
        for (int i = 5; n / i >= 1; i *= 5)
            count += n / i;
 
        return count;
    }

    private void LongestX() {
//  Given is a string S consisting of X and ..
//  You can do the following operation on S between 0 and K times (inclusive).
//  Replace a . with an X.
//  What is the maximum possible number of consecutive Xs in S after the operations?
        char[] s = ns().toCharArray();
        int K = ni();
        int n = s.length;
        int[] cum = new int[n+1];
        cum[0] = 0;
        for(int i = 0;i < n;i++){
            cum[i+1] = cum[i] + (s[i] == '.' ? 1 : 0);
        }
 
        int low = -1;
        int high = s.length + 1;
        outer:
        while(high - low > 1){
            int h = high + low >> 1;
            for(int i = 0;i+h <= n;i++){
                if(cum[i+h] - cum[i] <= K){
                    low = h;
                    continue outer;
                }
            }
            high = h;
        }
        out.println(low);
    }

    private long calculate_Xor(long n) 
    {
        if(n%4 == 0) return n;
        else if(n%4 == 1) return 1;
        else if(n%4 == 2) return n+1;
        return 0;
    }

    private class Pair {
        int first;
        int second;
        Pair(int a, int b)
        {
            first = a;
            second = b;
        }
    }

    private String swap(String s , int i , int j ) 
    {
        StringBuilder str = new StringBuilder(s);
        char l = str.charAt(i) , r = str.charAt(j);
        str.setCharAt(i,r);
        str.setCharAt(j,l);
        return str.toString();
    }
/*****************************************************************************************************/
    void solve()
    {
        int t = ni();
        while(t-- > 0)
        {
            int n = ni();
            String s = ""; String p = "";
            do{s=ns();}while(s.length()!=n);
            do{p=ns();}while(p.length()!=n);
            boolean f = false;
            for(int i=0; i<n; i++)
            {
                if(s.charAt(i) == '1')
                {
                    f = true;
                    break;
                }
            }
            if(f)
            {
                int c1 = 0, c2 = 0;
                for(int i=0; i<n; i++)
                {
                    if((s.charAt(i) == '1' && p.charAt(i) == '0')||(s.charAt(i) == '0' && p.charAt(i) == '1'))
                        c1++;
                    if((s.charAt(i) == '1' && p.charAt(i) == '1')||(s.charAt(i) == '0' && p.charAt(i) == '0'))
                        c2++;
                }
                out.println(Math.min(c1, c2));
            }
            else
            {
                out.println(-1);
            }
        }
    }
/******************************************************************************************************/ 
    public static class FastWriter
    {
        private static final int BUF_SIZE = 1<<13;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;
 
        private FastWriter(){out = null;}
 
        public FastWriter(OutputStream os)
        {
            this.out = os;
        }
 
        public FastWriter(String path)
        {
            try {
                this.out = new FileOutputStream(path);
            } catch (FileNotFoundException e) {
                throw new RuntimeException("FastWriter");
            }
        }
 
        public FastWriter write(byte b)
        {
            buf[ptr++] = b;
            if(ptr == BUF_SIZE)innerflush();
            return this;
        }
 
        public FastWriter write(char c)
        {
            return write((byte)c);
        }
 
        public FastWriter write(char[] s)
        {
            for(char c : s){
                buf[ptr++] = (byte)c;
                if(ptr == BUF_SIZE)innerflush();
            }
            return this;
        }
 
        public FastWriter write(String s)
        {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte)c;
                if(ptr == BUF_SIZE)innerflush();
            });
            return this;
        }
 
        private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }
 
        public FastWriter write(int x)
        {
            if(x == Integer.MIN_VALUE){
                return write((long)x);
            }
            if(ptr + 12 >= BUF_SIZE)innerflush();
            if(x < 0){
                write((byte)'-');
                x = -x;
            }
            int d = countDigits(x);
            for(int i = ptr + d - 1;i >= ptr;i--){
                buf[i] = (byte)('0'+x%10);
                x /= 10;
            }
            ptr += d;
            return this;
        }
 
        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }
 
        public FastWriter write(long x)
        {
            if(x == Long.MIN_VALUE){
                return write("" + x);
            }
            if(ptr + 21 >= BUF_SIZE)innerflush();
            if(x < 0){
                write((byte)'-');
                x = -x;
            }
            int d = countDigits(x);
            for(int i = ptr + d - 1;i >= ptr;i--){
                buf[i] = (byte)('0'+x%10);
                x /= 10;
            }
            ptr += d;
            return this;
        }
 
        public FastWriter write(double x, int precision)
        {
            if(x < 0){
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision)/2;
            //      if(x < 0){ x = 0; }
            write((long)x).write(".");
            x -= (long)x;
            for(int i = 0;i < precision;i++){
                x *= 10;
                write((char)('0'+(int)x));
                x -= (int)x;
            }
            return this;
        }
 
        public FastWriter writeln(char c){
            return write(c).writeln();
        }
 
        public FastWriter writeln(int x){
            return write(x).writeln();
        }
 
        public FastWriter writeln(long x){
            return write(x).writeln();
        }
 
        public FastWriter writeln(double x, int precision){
            return write(x, precision).writeln();
        }
 
        public FastWriter write(int... xs)
        {
            boolean first = true;
            for(int x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }
 
        public FastWriter write(long... xs)
        {
            boolean first = true;
            for(long x : xs) {
                if (!first) write(' ');
                first = false;
                write(x);
            }
            return this;
        }
 
        public FastWriter writeln()
        {
            return write((byte)'\n');
        }
 
        public FastWriter writeln(int... xs)
        {
            return write(xs).writeln();
        }
 
        public FastWriter writeln(long... xs)
        {
            return write(xs).writeln();
        }
 
        public FastWriter writeln(char[] line)
        {
            return write(line).writeln();
        }
 
        public FastWriter writeln(char[]... map)
        {
            for(char[] line : map)write(line).writeln();
            return this;
        }
 
        public FastWriter writeln(String s)
        {
            return write(s).writeln();
        }
 
        private void innerflush()
        {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }
 
        public void flush()
        {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }
 
        public FastWriter print(byte b) { return write(b); }
        public FastWriter print(char c) { return write(c); }
        public FastWriter print(char[] s) { return write(s); }
        public FastWriter print(String s) { return write(s); }
        public FastWriter print(int x) { return write(x); }
        public FastWriter print(long x) { return write(x); }
        public FastWriter print(double x, int precision) { return write(x, precision); }
        public FastWriter println(char c){ return writeln(c); }
        public FastWriter println(int x){ return writeln(x); }
        public FastWriter println(long x){ return writeln(x); }
        public FastWriter println(double x, int precision){ return writeln(x, precision); }
        public FastWriter print(int... xs) { return write(xs); }
        public FastWriter print(long... xs) { return write(xs); }
        public FastWriter println(int... xs) { return writeln(xs); }
        public FastWriter println(long... xs) { return writeln(xs); }
        public FastWriter println(char[] line) { return writeln(line); }
        public FastWriter println(char[]... map) { return writeln(map); }
        public FastWriter println(String s) { return writeln(s); }
        public FastWriter println() { return writeln(); }
    }
 
    public void trnz(int... o)
    {
        for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
        System.out.println();
    }
 
    // print ids which are 1
    public void trt(long... o)
    {
        Queue<Integer> stands = new ArrayDeque<>();
        for(int i = 0;i < o.length;i++){
            for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
        }
        System.out.println(stands);
    }
 
    public void tf(boolean... r)
    {
        for(boolean x : r)System.out.print(x?'#':'.');
        System.out.println();
    }
 
    public void tf(boolean[]... b)
    {
        for(boolean[] r : b) {
            for(boolean x : r)System.out.print(x?'#':'.');
            System.out.println();
        }
        System.out.println();
    }
 
    public void tf(long[]... b)
    {
        if(INPUT.length() != 0) {
            for (long[] r : b) {
                for (long x : r) {
                    for (int i = 0; i < 64; i++) {
                        System.out.print(x << ~i < 0 ? '#' : '.');
                    }
                }
                System.out.println();
            }
            System.out.println();
        }
    }
 
    public void tf(long... b)
    {
        if(INPUT.length() != 0) {
            for (long x : b) {
                for (int i = 0; i < 64; i++) {
                    System.out.print(x << ~i < 0 ? '#' : '.');
                }
            }
            System.out.println();
        }
    }
}