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.IOException;
import java.io.InputStream;
import java.util.*;

public class C {

  /**
   * Template @author William Fiset, william.alexandre.fiset@gmail.com
   *
   */
  static InputReader in = new InputReader(System.in);
  private static StringBuilder sb;

  static class InputReader {

    private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
    private static final InputStream DEFAULT_STREAM = System.in;
    private static final int MAX_DECIMAL_PRECISION = 21;
    private int c;
    private byte[] buf;
    private int bufferSize, bufIndex, numBytesRead;

    private InputStream stream;

    private static final byte EOF = -1;
    private static final byte NEW_LINE = 10;
    private static final byte SPACE = 32;
    private static final byte DASH = 45;
    private static final byte DOT = 46;

    private char[] charBuffer;

    private static byte[] bytes = new byte[58];
    private static int[] ints = new int[58];
    private static char[] chars = new char[128];

    static {
      char ch = ' ';
      int value = 0;
      byte _byte = 0;
      for (int i = 48; i < 58; i++) {
        bytes[i] = _byte++;
      }
      for (int i = 48; i < 58; i++) {
        ints[i] = value++;
      }
      for (int i = 32; i < 128; i++) {
        chars[i] = ch++;
      }
    }

    private static final double[][] doubles = {
      {0.0d, 0.00d, 0.000d, 0.0000d, 0.00000d, 0.000000d, 0.0000000d, 0.00000000d, 0.000000000d,
        0.0000000000d, 0.00000000000d, 0.000000000000d,
        0.0000000000000d, 0.00000000000000d, 0.000000000000000d, 0.0000000000000000d,
        0.00000000000000000d, 0.000000000000000000d,
        0.0000000000000000000d, 0.00000000000000000000d, 0.000000000000000000000d},
      {0.1d, 0.01d, 0.001d, 0.0001d, 0.00001d, 0.000001d, 0.0000001d, 0.00000001d, 0.000000001d,
        0.0000000001d, 0.00000000001d, 0.000000000001d,
        0.0000000000001d, 0.00000000000001d, 0.000000000000001d, 0.0000000000000001d,
        0.00000000000000001d, 0.000000000000000001d,
        0.0000000000000000001d, 0.00000000000000000001d, 0.000000000000000000001d},
      {0.2d, 0.02d, 0.002d, 0.0002d, 0.00002d, 0.000002d, 0.0000002d, 0.00000002d, 0.000000002d,
        0.0000000002d, 0.00000000002d, 0.000000000002d,
        0.0000000000002d, 0.00000000000002d, 0.000000000000002d, 0.0000000000000002d,
        0.00000000000000002d, 0.000000000000000002d,
        0.0000000000000000002d, 0.00000000000000000002d, 0.000000000000000000002d},
      {0.3d, 0.03d, 0.003d, 0.0003d, 0.00003d, 0.000003d, 0.0000003d, 0.00000003d, 0.000000003d,
        0.0000000003d, 0.00000000003d, 0.000000000003d,
        0.0000000000003d, 0.00000000000003d, 0.000000000000003d, 0.0000000000000003d,
        0.00000000000000003d, 0.000000000000000003d,
        0.0000000000000000003d, 0.00000000000000000003d, 0.000000000000000000003d},
      {0.4d, 0.04d, 0.004d, 0.0004d, 0.00004d, 0.000004d, 0.0000004d, 0.00000004d, 0.000000004d,
        0.0000000004d, 0.00000000004d, 0.000000000004d,
        0.0000000000004d, 0.00000000000004d, 0.000000000000004d, 0.0000000000000004d,
        0.00000000000000004d, 0.000000000000000004d,
        0.0000000000000000004d, 0.00000000000000000004d, 0.000000000000000000004d},
      {0.5d, 0.05d, 0.005d, 0.0005d, 0.00005d, 0.000005d, 0.0000005d, 0.00000005d, 0.000000005d,
        0.0000000005d, 0.00000000005d, 0.000000000005d,
        0.0000000000005d, 0.00000000000005d, 0.000000000000005d, 0.0000000000000005d,
        0.00000000000000005d, 0.000000000000000005d,
        0.0000000000000000005d, 0.00000000000000000005d, 0.000000000000000000005d},
      {0.6d, 0.06d, 0.006d, 0.0006d, 0.00006d, 0.000006d, 0.0000006d, 0.00000006d, 0.000000006d,
        0.0000000006d, 0.00000000006d, 0.000000000006d,
        0.0000000000006d, 0.00000000000006d, 0.000000000000006d, 0.0000000000000006d,
        0.00000000000000006d, 0.000000000000000006d,
        0.0000000000000000006d, 0.00000000000000000006d, 0.000000000000000000006d},
      {0.7d, 0.07d, 0.007d, 0.0007d, 0.00007d, 0.000007d, 0.0000007d, 0.00000007d, 0.000000007d,
        0.0000000007d, 0.00000000007d, 0.000000000007d,
        0.0000000000007d, 0.00000000000007d, 0.000000000000007d, 0.0000000000000007d,
        0.00000000000000007d, 0.000000000000000007d,
        0.0000000000000000007d, 0.00000000000000000007d, 0.000000000000000000007d},
      {0.8d, 0.08d, 0.008d, 0.0008d, 0.00008d, 0.000008d, 0.0000008d, 0.00000008d, 0.000000008d,
        0.0000000008d, 0.00000000008d, 0.000000000008d,
        0.0000000000008d, 0.00000000000008d, 0.000000000000008d, 0.0000000000000008d,
        0.00000000000000008d, 0.000000000000000008d,
        0.0000000000000000008d, 0.00000000000000000008d, 0.000000000000000000008d},
      {0.9d, 0.09d, 0.009d, 0.0009d, 0.00009d, 0.000009d, 0.0000009d, 0.00000009d, 0.000000009d,
        0.0000000009d, 0.00000000009d, 0.000000000009d,
        0.0000000000009d, 0.00000000000009d, 0.000000000000009d, 0.0000000000000009d,
        0.00000000000000009d, 0.000000000000000009d,
        0.0000000000000000009d, 0.00000000000000000009d, 0.000000000000000000009d}
    };

    public InputReader() {
      this(DEFAULT_STREAM, DEFAULT_BUFFER_SIZE);
    }

    public InputReader(int bufferSize) {
      this(DEFAULT_STREAM, bufferSize);
    }

    public InputReader(InputStream stream) {
      this(stream, DEFAULT_BUFFER_SIZE);
    }

    public InputReader(InputStream stream, int bufferSize) {
      if (stream == null || bufferSize <= 0) {
        throw new IllegalArgumentException();
      }
      buf = new byte[bufferSize];
      charBuffer = new char[128];
      this.bufferSize = bufferSize;
      this.stream = stream;
    }

    private byte read() throws IOException {

      if (numBytesRead == EOF) {
        throw new IOException();
      }

      if (bufIndex >= numBytesRead) {
        bufIndex = 0;
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return EOF;
        }
      }

      return buf[bufIndex++];
    }

    private void doubleCharBufferSize() {
      char[] newBuffer = new char[charBuffer.length << 1];
      for (int i = 0; i < charBuffer.length; i++) {
        newBuffer[i] = charBuffer[i];
      }
      charBuffer = newBuffer;
    }

    private int readJunk(int token) throws IOException {

      if (numBytesRead == EOF) {
        return EOF;
      }

      do {

        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > token) {
            return 0;
          }
          bufIndex++;
        }

        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return EOF;
        }
        bufIndex = 0;

      } while (true);

    }

    public byte nextByte() throws IOException {
      return (byte) nextInt();
    }

    public int nextInt() throws IOException {

      if (readJunk(DASH - 1) == EOF) {
        throw new IOException();
      }
      int sgn = 1, res = 0;

      c = buf[bufIndex];
      if (c == DASH) {
        sgn = -1;
        bufIndex++;
      }

      do {

        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            res = (res << 3) + (res << 1);
            res += ints[buf[bufIndex++]];
          } else {
            bufIndex++;
            return res * sgn;
          }
        }

        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return res * sgn;
        }
        bufIndex = 0;

      } while (true);

    }

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

    public void close() throws IOException {
      stream.close();
    }

    public long nextLong() throws IOException {
      if (readJunk(DASH - 1) == EOF) {
        throw new IOException();
      }
      int sgn = 1;
      long res = 0L;
      c = buf[bufIndex];
      if (c == DASH) {
        sgn = -1;
        bufIndex++;
      }
      do {
        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            res = (res << 3) + (res << 1);
            res += ints[buf[bufIndex++]];
          } else {
            bufIndex++;
            return res * sgn;
          }
        }
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return res * sgn;
        }
        bufIndex = 0;
      } while (true);
    }

    public String nextString() throws IOException {
      if (numBytesRead == EOF) {
        return null;
      }
      if (readJunk(SPACE) == EOF) {
        return null;
      }

      for (int i = 0;;) {
        while (bufIndex < numBytesRead) {
          if (buf[bufIndex] > SPACE) {
            if (i == charBuffer.length) {
              doubleCharBufferSize();
            }
            charBuffer[i++] = (char) buf[bufIndex++];
          } else {
            bufIndex++;
            return new String(charBuffer, 0, i);
          }
        }

        // Reload buffer
        numBytesRead = stream.read(buf);
        if (numBytesRead == EOF) {
          return new String(charBuffer, 0, i);
        }
        bufIndex = 0;
      }
    }
  }

  public static void main(String args[]) throws Exception {
    int t = in.nextInt();
    while (t-- != 0) {
      solve();
    }
  }

  static void solve() throws IOException {
    int n = in.nextInt();
    String a, b;
    a = in.nextString();
    b = in.nextString();
    int x = 0, y = 0, s = 0, t = 0;
    int diff = 0;
    boolean canSwap = false;
    for (int i = 0; i < n; i++) {
      if (a.charAt(i) != b.charAt(i)) {
        diff++;
      }
    }
    for (char c : a.toCharArray()) {
      if (c == '0') {
        y++;
      } else {
        canSwap = true;
        x++;
      }
    }
    for (char c : b.toCharArray()) {
      if (c == '0') {
        t++;
      } else {
        s++;
      }
    }
    boolean valid = (diff ==0)  || (canSwap && (x == s || y + 1 == s));
    int min = Integer.MAX_VALUE;
    if (x == s) {
      if (diff %2 != 0 && (n - diff) % 2 != 0) {
        valid = valid || false;
      }
      if (diff % 2 == 0) {
        min = Math.min(min, diff);
      }
      if ((n - diff) % 2 == 0) {
        min = Math.min(min, n-diff);
      }
    }
    if (y + 1 == s) {
      if (diff %2 == 0 && (n - diff) % 2 == 0) {
        valid = valid || false;
      }
      if (diff % 2 != 0) {
        min = Math.min(min, diff);
      }
      if ((n - diff) % 2 != 0) {
        min = Math.min(min, n-diff);
      }
    }
    System.out.println(valid ? min : -1);
  }

}
