Consider a simplified penalty phase at the end of a football match.

A penalty phase consists of at most 10 kicks, the first team takes the first kick, the second team takes the second kick, then the first team takes the third kick, and so on. The team that scores more goals wins; if both teams score the same number of goals, the game results in a tie (note that it goes against the usual football rules). The penalty phase is stopped if one team has scored more goals than the other team could reach with all of its remaining kicks. For example, if after the 7-th kick the first team has scored 1 goal, and the second team has scored 3 goals, the penalty phase ends — the first team cannot reach 3 goals.

You know which player will be taking each kick, so you have your predictions for each of the 10 kicks. These predictions are represented by a string s consisting of 10 characters. Each character can either be 1, 0, or ?. This string represents your predictions in the following way:

  * if s_i is 1, then the i-th kick will definitely score a goal; 
  * if s_i is 0, then the i-th kick definitely won't score a goal; 
  * if s_i is ?, then the i-th kick could go either way. 



Based on your predictions, you have to calculate the minimum possible number of kicks there can be in the penalty phase (that means, the earliest moment when the penalty phase is stopped, considering all possible ways it could go). Note that the referee doesn't take into account any predictions when deciding to stop the penalty phase — you may know that some kick will/won't be scored, but the referee doesn't.

Input

The first line contains one integer t (1 ≤ t ≤ 1 000) — the number of test cases.

Each test case is represented by one line containing the string s, consisting of exactly 10 characters. Each character is either 1, 0, or ?.

Output

For each test case, print one integer — the minimum possible number of kicks in the penalty phase.

Example

Input


4
1?0???1001
1111111111
??????????
0100000000


Output


7
10
6
9

Note

Consider the example test:

In the first test case, consider the situation when the 1-st, 5-th and 7-th kicks score goals, and kicks 2, 3, 4 and 6 are unsuccessful. Then the current number of goals for the first team is 3, for the second team is 0, and the referee sees that the second team can score at most 2 goals in the remaining kicks. So the penalty phase can be stopped after the 7-th kick.

In the second test case, the penalty phase won't be stopped until all 10 kicks are finished.

In the third test case, if the first team doesn't score any of its three first kicks and the second team scores all of its three first kicks, then after the 6-th kick, the first team has scored 0 goals and the second team has scored 3 goals, and the referee sees that the first team can score at most 2 goals in the remaining kicks. So, the penalty phase can be stopped after the 6-th kick.

In the fourth test case, even though you can predict the whole penalty phase, the referee understands that the phase should be ended only after the 9-th kick.
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;

public class A
{
    static int n;
    static int[] arr;
    static char[] s;
    public static void main(String[] args) throws IOException
    {
        f = new Flash();
        out = new PrintWriter(System.out);
        
        int T = ni();
        for(int tc = 1; tc <= T; tc++){
        	s = nc(); sop(fn());
        }
        
        out.flush(); out.close();
    }
    
    static int fn()
    {
    	int ans = 10;
    	int g1 = 0, g2 = 0, d1 = 0, d2 = 0;
        for(int i = 0; i < 10; i++) {
        	if(i%2 == 0) {
        		if(s[i] == '1' || s[i] == '?') g1++;
        		d1++;
        	} else {
        		if(s[i] == '1') g2++;
        		d2++;
        	}
        	
        	if(g1 > g2) {
        		if(g1 > g2+(5-d2)) ans = min(ans, i+1);
        	}
        	
        	else if(g2 > g1) {
        		if(g2 > g1+(5-d1)) ans = min(ans, i+1);
        	}
        }
        
        g1 = 0; g2 = 0; d1 = 0; d2 = 0;
        for(int i = 0; i < 10; i++) {
        	if(i%2 == 0) {
        		if(s[i] == '1') g1++;
        		d1++;
        	} else {
        		if(s[i] == '1' || s[i] == '?') g2++;
        		d2++;
        	}
        	
        	if(g1 > g2) {
        		if(g1 > g2+(5-d2)) ans = min(ans, i+1);
        	}
        	
        	else if(g2 > g1) {
        		if(g2 > g1+(5-d1)) ans = min(ans, i+1);
        	}
        	
        	//sop("g1 = " + g1 + " g2 = " + g2);
        }
        
        return ans;
    }
    
    static Flash f;
    static PrintWriter out;
    static final long mod = (long)1e9+7;
    static final long inf = (long)1e18;
    static final int _inf = (int)1e9;
    static final int maxN = (int)1e6;
    static long[] fact, inv;
    
    static class cpr implements Comparator<int[]>{
    	public int compare(int[] a, int[] b) {
    		return Integer.compare(a[0], b[0]);
    	}
    }
    
    static void sort(int[] a){
        List<Integer> A = new ArrayList<>();
        for(int i : a) A.add(i);
        Collections.sort(A);
        for(int i = 0; i < A.size(); i++) a[i] = A.get(i);
    }
    
    static void sort(long[] a){
        List<Long> A = new ArrayList<>();
        for(long i : a) A.add(i);
        Collections.sort(A);
        for(int i = 0; i < A.size(); i++) a[i] = A.get(i);
    }
    
    static void print(int[] a){
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < a.length; i++) sb.append(a[i] + " ");
        sop(sb);
    }
    
    static void print(long[] a){
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < a.length; i++) sb.append(a[i] + " ");
        sop(sb);
    }
    
    static int swap(int itself, int dummy){return itself;}
    static long swap(long itself, long dummy){return itself;}
    static char swap(char itself, char dummy){return itself;}
    static void sop(Object o){out.println(o);}
    static int ni(){return f.ni();}
    static long nl(){return f.nl();}
    static double nd(){return f.nd();}
    static String next(){return f.next();}
    static String ns(){return f.ns();}
    static String yes = "YES", no = "NO";
    static char[] nc(){return f.nc();}
    static int[] arr(int len){return f.arr(len);}
    static int gcd(int a, int b){if(b == 0) return a; return gcd(b, a%b);}
    static long gcd(long a, long b){if(b == 0) return a; return gcd(b, a%b);}
    static int fcm(int a, int b){return (a*b)/gcd(a, b);}
    static long fcm(long a, long b){return (a*b)/gcd(a, b);}
    static double log2(long N) {return Math.log(N) / Math.log(2);}
    static void debug(int[] a) {sop(Arrays.toString(a));}
    static void debug(long[] a) {sop(Arrays.toString(a));}
    
    static class Flash
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        
        String next(){
            while(!st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){
                    e.printStackTrace();
                }
            }
            
            return st.nextToken();
        }
        
        String ns(){
            String s = new String();
            try{
                s = br.readLine().trim();
            }catch(IOException e){
                e.printStackTrace();
            }
            
            return s;
        }
        
        int[] arr(int n){
            int[] a = new int[n];
            for(int i = 0; i < n; i++) a[i] = ni();
            return a;
        }
        
        char[] nc(){return ns().toCharArray();}
        int ni(){return Integer.parseInt(next());}
        long nl(){return Long.parseLong(next());}
        double nd(){return Double.parseDouble(next());}
    }
}