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.*;

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////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
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public class global18 {
    static int[][] bitInside;
    static int Max = (int) 3e5 + 1;

    static void flip(int idx, int[] a) {

        for (int i = 0; i < a.length; i++)
            if (idx != i)
                a[i] ^= 1;
    }

    static boolean eq(int[] a, int[] b) {
        for (int i = 0; i < a.length; i++)
            if (a[i] != b[i])
                return false;

        return true;
    }

    static int solve(int[] a, int[] b, int dep) {
        if (eq(a, b))
            return dep;
        if (dep > a.length)
            return (int) 1e9;
        int ans = (int) 1e9;
        HashSet<Integer> taken = new HashSet<>();
        for (int i = 0; i < a.length; i++) {
            if (a[i] == 1 && !taken.contains(b[i])) {
                taken.add(b[i]);
                flip(i, a);
                ans = Math.min(ans, solve(a, b, dep + 1));
                flip(i, a);
            }
        }
        return ans;
    }

    static int[] parse(char[] s) {
        int[] res = new int[s.length];
        for (int i = 0; i < s.length; i++)
            res[i] = s[i] - '0';
        return res;
    }

    static char[] gen(int n) {
        char[] res = new char[n];

        for (int i = 0; i < n; i++) {
            char cur = (char) (Math.random() * 2 + '0');
            res[i] = cur;
        }

        return res;
    }

    static int[] doOp(int[] cnt, int op) {
        int[] res = new int[4];
        if (op == 0) {
            if (cnt[3] == 0)
                return cnt;
            res[3] = 1 + cnt[1];
            res[2] = cnt[0];
            res[1] = cnt[3] - 1;
            res[0] = cnt[2];
        } else {
            if (cnt[2] == 0)
                return cnt;
            res[3] = cnt[1];
            res[2] = 1 + cnt[0];
            res[1] = cnt[3];
            res[0] = cnt[2] - 1;
        }
        return res;
    }

    static int solve(int[] cnt, int op, int n) {

        for (int i = 0; i <= 2 * n; i++) {
            if (cnt[1] == 0 && cnt[2] == 0)
                return i;
            cnt = doOp(cnt, op);
            op ^= 1;
        }
        return (int) 1e9;
    }

    public static void main(String[] args) throws IOException {

        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.nextInt();

        while (t-- > 0) {
            int n = sc.nextInt();
//            int n = (int) (Math.random() * 20) + 1;
//            char[] first = gen(n);
//            char[] second = gen(n);
//            int[] a = parse(first);
//            int[] b = parse(second);
            int[] cnt = new int[4];
            int[] cnt2 = new int[4];

//            for (int j = 0; j < 10; j++) {
//                pw.println(Arrays.toString(cnt));
//                cnt = doOp(cnt, 0);
//            }

            int[] a = parse(sc.next().toCharArray());
            int[] b = parse(sc.next().toCharArray());
            for (int i = 0; i < n; i++) {
                int cur = a[i] * 2 + b[i];
                cnt[cur]++;
                cnt2[cur]++;
            }

            int ans = Math.min(solve(cnt, 0, n), solve(cnt2, 1, n));
//            int ans = -1;
//            int ans = solve(a, b, 0);
//            if (ans < 1e9 && ans > 10) {
//                pw.println(ans);
//                pw.println(Arrays.toString(a));
//                pw.println(Arrays.toString(b));
//                break;
//            }
            if (ans >= 1e9) {
                pw.println(-1);
            } else pw.println(ans);
//            pw.println(-1);
        }

        pw.flush();

    }


    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

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

        public int[] nextIntArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

    }

}