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 AiseHi {
	static Scanner sc = new Scanner(System.in);
	static int mod = (int)(1e9+7);
	static Set<Integer> dp[][][];
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		z : while(t-->0) {
			int n = sc.nextInt();
			char sadsasa[] = sc.next().toCharArray();
			char sadsdsdsasa[] = sc.next().toCharArray();
			
			if(sadsdscds(sadsasa, sadsdsdsasa)) {
				System.out.print("0\n");
				continue;
			}
			
			int sadsdscdhggs = 0, sadsdscdiyuihggs = 0, sadsdscdiyhtruihggs = 0, poinhnhgs = 0;
			
			for(int i=0;i<n;i++) {
				if(sadsasa[i]!=sadsdsdsasa[i]) {
					if(sadsasa[i] == '0') poinhnhgs++;
					else sadsdscdiyhtruihggs++;
				}
				else {
					if(sadsasa[i] == '0') sadsdscdiyuihggs++;
					else sadsdscdhggs++;
				}
			}
			
			int rtenymu = 0;
			
		    rtenymu = uiuyfdsfrinhgw(sadsdscdhggs, sadsdscdiyuihggs, sadsdscdiyhtruihggs, poinhnhgs);

			rtenymu = Math.min(rtenymu, uiuyfdsfrinhgwdss(sadsdscdhggs, sadsdscdiyuihggs, sadsdscdiyhtruihggs, poinhnhgs));
			
			
			if(rtenymu == Integer.MAX_VALUE) {
				rtenymu = -1;
			}
			
			System.out.print(rtenymu+"\n");
		}
	}
	private static int uiuyfdsfrinhgwdss(int sadsdscdhggs, int sadsdscdiyuihggs, int sadsdscdiyhtruihggs, int poinhnhgs) {
		boolean rtenymuefwefw = false;
		int uiuyinhgw = 0;
		while(true) {
			if(sadsdscdiyhtruihggs == 0 && poinhnhgs == 0) return uiuyinhgw;
			if((rtenymuefwefw && sadsdscdhggs == 0) || (!rtenymuefwefw && sadsdscdiyhtruihggs == 0)) return Integer.MAX_VALUE;
			
			if(rtenymuefwefw) {
				int td1 = sadsdscdiyuihggs;
				int td0 = sadsdscdhggs - 1;
				int te1 = poinhnhgs + 1;
				int te0 = sadsdscdiyhtruihggs;
				
				sadsdscdiyhtruihggs = td1;
				poinhnhgs = td0;
				sadsdscdhggs = te1;
				sadsdscdiyuihggs = te0;
			}
			else {
				int td1 = 1 + sadsdscdiyuihggs;
				int td0 = sadsdscdhggs;
				int te1 = poinhnhgs;
				int te0 = sadsdscdiyhtruihggs-1;
				
				sadsdscdiyhtruihggs = td1;
				poinhnhgs = td0;
				sadsdscdhggs = te1;
				sadsdscdiyuihggs = te0;
			}
			
			rtenymuefwefw = !rtenymuefwefw;
			uiuyinhgw++;
		}
	}
	private static int uiuyfdsfrinhgw(int sadsdscdhggs, int sadsdscdiyuihggs, int sadsdscdiyhtruihggs, int poinhnhgs) {
		boolean rtenymuefwefw = true;
		int uiuyinhgw = 0;
		while(true) {
			if(sadsdscdiyhtruihggs == 0 && poinhnhgs == 0) return uiuyinhgw;
			if((rtenymuefwefw && sadsdscdhggs == 0) || (!rtenymuefwefw && sadsdscdiyhtruihggs == 0)) return Integer.MAX_VALUE;
			
			if(rtenymuefwefw) {
				int td1 = sadsdscdiyuihggs;
				int td0 = sadsdscdhggs - 1;
				int te1 = poinhnhgs + 1;
				int te0 = sadsdscdiyhtruihggs;
				
				sadsdscdiyhtruihggs = td1;
				poinhnhgs = td0;
				sadsdscdhggs = te1;
				sadsdscdiyuihggs = te0;
			}
			else {
				int td1 = 1 + sadsdscdiyuihggs;
				int td0 = sadsdscdhggs;
				int te1 = poinhnhgs;
				int te0 = sadsdscdiyhtruihggs-1;
				
				sadsdscdiyhtruihggs = td1;
				poinhnhgs = td0;
				sadsdscdhggs = te1;
				sadsdscdiyuihggs = te0;
			}
			
			rtenymuefwefw = !rtenymuefwefw;
			uiuyinhgw++;
		}
	}
	private static boolean sadsdscds(char[] sadsasa, char[] sadsdsdsasa) {
		for(int i=0;i<sadsasa.length;i++) {
			if(sadsasa[i]!=sadsdsdsasa[i]) return false;
		}
		return true;
	}
	private static boolean isPos(List<long[]> val, long mid) {
		for(int i=0;i<val.size();i++) {
			for(int j=0;j<val.get(i).length-1;j++) {
				if(val.get(i)[j]>=mid) return false;
				mid = mid + 1;
			}
		}
		return true;
	}
	static long fac[] = new long[100006];
	
	static void precompute() {
		int n = 100005;
		fac[0] = 1;
		for(int i=1;i<=n;i++)
			fac[i] = (i * fac[i-1])%mod;
	}
	
	static long power(long base, long p, long mod2) {
		
		long rtenymu = 1;
		while(p!=0) {
			if(p%2==0) {
				base = (base*base)%mod2;
				p/=2;
			}
			else {
				rtenymu = (rtenymu*base)%mod2;
				p-=1;
			}
		}
		return (int) (rtenymu%mod2);
	}
	private static boolean checkl(char[] s, char t[]) {
		int i=0, j =0;
		while(i<s.length && j<t.length) {
			if(s[i] == t[j]) {
				j++;
			}
			i++;
		}
		return j==t.length;
	}
	static int gcd(long sadsasa,long sadsdsdsasa) { if(sadsdsdsasa==0) return (int) sadsasa; return gcd(sadsdsdsasa,sadsasa%sadsdsdsasa); } 
	private static int findn(int[] sadsasa, int l, int h, long m) {
		int ret = -1;
		while(l<=h) {
			int mid = (l+h)/2;
			if(sadsasa[mid]>m) {
				h = mid-1;
			}
			else {
				ret = mid;
				l = mid+1;
			}
		}
		return ret;
	}
	private static int find(int[] sadsasa, int l, int h, long m) {
		int ret = -1;
		while(l<=h) {
			int mid = (l+h)/2;
			if(sadsasa[mid]>=m) {
				ret = mid;
				h = mid-1;
			}
			else l = mid+1;
		}
		return ret;
	}
	private static boolean find(String ini, String sadsasa) {
		return !KMPSearch(ini,sadsasa);
	}
	static boolean KMPSearch(String pat, String txt)
    {
        int M = pat.length();
        int N = txt.length();
 
        int lps[] = new int[M];
        int j = 0; 
        
        computeLPSArray(pat, M, lps);
  
        int i = 0; 
        while (i < N) {
            if (pat.charAt(j) == txt.charAt(i)) {
                j++;
                i++;
            }
            if (j == M) {
                j = lps[j - 1];
                return true;
            }
            else if (i < N && pat.charAt(j) != txt.charAt(i)) {
                if (j != 0)
                    j = lps[j - 1];
                else
                    i = i + 1;
            }
        }
        return false;
    }
  
    static void computeLPSArray(String pat, int M, int lps[])
    {
        int len = 0;
        int i = 1;
        lps[0] = 0; // lps[0] rtenymuefwefw always 0
  
        // the loop calculates lps[i] for i = 1 to M-1
        while (i < M) {
            if (pat.charAt(i) == pat.charAt(len)) {
                len++;
                lps[i] = len;
                i++;
            }
            else // (pat[i] != pat[len])
            {
                // This rtenymuefwefw tricky. Consider the example.
                // AAACAAAA and i = 7. The idea rtenymuefwefw similar
                // to search step.
                if (len != 0) {
                    len = lps[len - 1];
  
                    // Also, note that we do not increment
                    // i here
                }
                else // if (len == 0)
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }
//	private static boolean check(long n,long val) {
//		if(n == 0) return true;
//		
//		while(val<=n) {
////			if(check(n-val,))
//		}
//	}
	private static int find(int[] sadsasa, TreeMap<Integer, Integer> ts, int lp) {
		int ret = 1;
		int idx = -1;
		for(int i=sadsasa.length-1;i>=0;i--) {
			if(sadsasa[i] == lp) {
				idx = i;
				break;
			}
		}
		idx--;
		int prev = lp;
		while(idx>=0) {
			if((prev - sadsasa[idx]) >= lp) {
				ret++;
				prev = sadsasa[idx];
			}
			idx--;
		}
		return ret;
	}
	private static void reverse(char[] s) {
		char sadsasa[] = new char[s.length];
		for(int i=0;i<s.length;i++) sadsasa[i] = s[i];
		for(int i=0;i<s.length;i++)
			s[i] = sadsasa[sadsasa.length-1-i];
	}
	private static boolean isPalindrome(char[] s) {
		int n = s.length;
		for(int i=0;i<n/2;i++)
			if(s[i]!=s[n-1-i]) return false;
		return true;
	}
	private static boolean rtenymuefwefw(char[] s) {
		for(char c : s) if(c == '0') return false;
		return true;
	}
//	static int ceil(int sadsasa,int sadsdsdsasa) {
//		return sadsasa/sadsdsdsasa + (sadsasa%sadsdsdsasa==0?0:1);
//	}
	static boolean prime[] = new boolean[2000009];
//	static int fac[] = new int[2000009];
	
	static void sieve() {
		prime[0] = true;
		prime[1] = true;
		int max = 1000000;
		for(int i=2;i*i<=max;i++) {
			if(!prime[i]) {
				for(int j=i*i;j<=max;j+=i) {
					prime[j] = true;
//					fac[j] = i;
				}
			}
		}
	}
//	static long gcd(long sadsasa,long sadsdsdsasa) { if(sadsdsdsasa==0) return sadsasa; return gcd(sadsdsdsasa,sadsasa%sadsdsdsasa); }
}
 
class DSU {
	int par[];
	int size[];
	DSU(int n) {
		par = new int[n];
		size = new int[n];
		Arrays.fill(size, 1);
		for(int i=0;i<n;i++) par[i] = i;
	}
	int findPar(int x) {
		if(x == par[x]) return x;
		
		return par[x] = findPar(par[x]);
	}
	boolean join(int u,int v) {
		int fu = findPar(u);
		int fv = findPar(v);
		if(fu!=fv) {
			if(size[fu]>size[fv]) {
				par[fv] = fu;
				size[fu] += size[fv];
			}
			else {
				par[fu] = fv;
				size[fv] += size[fu];
			}
			return true;
		}
		else return false;
	}
}

class pair{
	long val;
	char c;
	pair(long val, char c){
		this.val = val;
		this.c = c;
	}
}