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.

 //   * * * the goal is to be worlds best * * *   //
 import java.io.BufferedReader;
 import java.io.IOException;
 import java.io.InputStreamReader;
 import java.util.*;
  
 
 public class C {
     static class Pair implements Comparable<Pair>{
         int a;
         int b;
 
         Pair(int a , int b){
             this.a = a;
             this.b = b;
         }
 
         public int compareTo(Pair o){
             return this.a - o.a;
         }
     }
 
 //==================================================================================================
 
     public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t = sc.nextInt();
        while(t-->0){
            String s = sc.nextLine();

            char ca[] = s.toCharArray();

            int ev = 0;
            int od = 0;
            int sec = 0;
            int first = 0;
            int ans = 10;
            for(int i = 0; i < s.length(); i++){  // firstWin
                if((i & 1) == 0){
                    if(ca[i] == '?'){
                        sec++;
                    }
                    else{
                        ev += ca[i] - '0';
                    }
                }
                
                else if((i & 1) == 1){ // 2nd team
                    if(ca[i] == '?'){
                        first++;
                    }
                    else{
                        od += ca[i] - '0';
                    }
                }
                if(od + first > ev + (9 - i) / 2){
                    ans = i + 1;
                    break;
                }
                if(ev + sec > od + (10 - i ) / 2){
                    ans = i + 1;
                    break;
                }
            }

            // for(int i = 0; i < 10; i++){  // secondWin
            //     if((i & 1) == 1){ // 2nd team
            //         if(ca[i] == '?'){
            //             secWin++;
            //         }
            //         else{
            //             secWin += ca[i] - '0';
            //         }
            //         if(secWin >= firstLoss + (9 - i) / 2){
            //             ans = Math.min(ans , i + 1);
            //         }
            //     }
            //     else{
            //         if(ca[i] == '?'){

            //         }
            //         else{
            //             firstLoss += ca[i] - '0';
            //         }
            //         if(secWin >= firstLoss + (9 - i + 1) / 2){
            //             ans = Math.min(ans , i + 1);
            //         }
            //     }
            // }
            
 
            System.out.println(ans);
        }
     }
 
 //==================================================================================================
 
 
     // Use this instead of Arrays.sort() on an array of ints. Arrays.sort() is n^2
     // worst case since it uses a version of quicksort. Although this would never
     // actually show up in the real world, in codeforces, people can hack, so
     // this is needed. 
	 static void sort(int[] arr) {
		 int n = arr.length;
		 ArrayList<Integer> res = new ArrayList<>();
		 for (int a : arr) {
		 	 res.add(a);
		 }
		 Collections.sort(res);
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		 }
	 }
 
	 static void sort(long[] arr) {
		 int n = arr.length;
		 ArrayList<Long> res = new ArrayList<>();
		 for (long a : arr) {
			 res.add(a);
		 }
		 Collections.sort(res);
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		} 
	 }
 
	 static void revSort(int[] arr) {
		 int n = arr.length;
		 ArrayList<Integer> res = new ArrayList<>();
		 for (int a : arr) {
			 res.add(a);
		 }
		 Collections.sort(res, Collections.reverseOrder());
		 for (int i = 0; i < n; i++) {
			 arr[i] = res.get(i);
		 }
	 } 
     
     // Use this to input code since it is faster than a Scanner
     static class FastScanner {
         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();
         }
         
         int nextInt() {
             return Integer.parseInt(next());
         }
 
         double nextDouble() {
             return Double.parseDouble(next());
         }
  
         String str = "";
  
         String nextLine() {
             try {
                 str = br.readLine();
             } catch (IOException e) {
                 e.printStackTrace();
             }
             return str;
         }
  
         int[] readArray(int n) {
             int[] a = new int[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextInt();
             return a;
         }
  
         long[] readLongArray(int n) {
             long[] a = new long[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextLong();
             return a;
         }
         long nextLong() {
             return Long.parseLong(next());
         }
     }
     
     // print integers in array
     static void print(int a[]){
         for(int e : a){
             System.out.print(e + " ");
         }
         System.out.println();
     }

     static void print(long a[]){
         for(long e : a){
             System.out.print(e + " ");
         }
         System.out.println();
     }

     // generates all the prime numbers upto n
     static void sieveOfEratosthenes(int n , ArrayList<Integer> al)
     {
         boolean prime[] = new boolean[n + 1];
         for (int i = 0; i <= n; i++)
             prime[i] = true;
  
         for (int p = 2; p * p <= n; p++) 
         {
             if (prime[p] == true) 
             {
                 for (int i = p * p; i <= n; i += p)
                     prime[i] = false;
             }
         }
         for (int i = 2; i <= n; i++)
         {
             if (prime[i] == true)
                 al.add(i);
         }
     }
     static final int mod = 1000_000_000 + 7;
     static final int imx = Integer.MAX_VALUE;
     static final int imi = Integer.MIN_VALUE;
     
	 static ArrayList<Integer> divisors(int n) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for (int i = 1; i * i <= n; i++) {
			 if (n % i == 0) {
				 if (n == i * i) {
					 al.add(i);
				 } else {
					 al.add(i);
					 al.add(n / i);
				 }
		 	 }
		 }
		 Collections.sort(al);
		 return al;
	 }
 
	 static int countDigits(int n) {
		 int c = 0;
		 while (n != 0) {
			 c++;
			 n /= 10;
		 }
		 return c;
	 }
 
	 static boolean palindrome(String str) {
		 int s = 0;
		 int e = str.length() - 1;
		 while (s < e) {
			 if (str.charAt(s) != str.charAt(e)) {
				 return false;
			 }
			 s++;
			 e--;
		 }
		 return true;
	 }
 
	 static void reverse(int[] arr, int s, int e) {
		 while (s < e) {
			 int temp = arr[s];
			 arr[s++] = arr[e];
			 arr[e--] = temp;
		 }
	 }
     // starting exclusive ending inclusive
	 static int getMax(int[] arr, int s, int e) {
		 int maxi = s;
		 for (int i = s + 1; i <= e; i++) {
			 if (arr[i] > arr[maxi]) {
				 maxi = i;
			 }
		 }
		 return maxi;
	 }

     // starting exclusive ending inclusive
     static int getMin(int[] arr, int s, int e) {
	     int mini = s;
		 for (int i = s + 1; i <= e; i++) {
			 if (arr[i] < arr[mini]) {
				 mini = i;
			 }
		 }
		 return mini;
	 }
 
	 static long lcm(long n1, long n2) {
		 return (n1 * n2) / gcd(n1, n2);
 	 }
 
	 static int lcm(int n1, int n2) {
		 return (n1 * n2) / gcd(n1, n2);
	 }
 
	 static long gcd(long num1, long num2) {
		 if (num2 == 0) {
			 return num1;
		 }
		 return gcd(num2, num1 % num2);
	 }
 
	 static int gcd(int num1, int num2) {
		 if (num2 == 0) {
			 return num1;
		 }
		 return gcd(num2, num1 % num2);
	 }

     //fastPow
     static long fastPow(long base, long exp) {
         if (exp==0) return 1;
         long half=fastPow(base, exp/2);
         if (exp%2==0) return mul(half, half);
         return mul(half, mul(half, base));
     }
 
     // multiply two long numbers % mod
     static long mul(long a, long b) {
         return a*b%mod;
     }
 
     static int nCr(int n, int r)
     {
        return factorial(n) / (factorial(r) *
            factorial(n - r));
     }
     
     // Returns factorial of n
     static int factorial(int n)
     {
         int res = 1;
         for (int i = 2; i <= n; i++)
             res = res * i;
         return res;
     }
      
     // to generate the lps array
     // lps means longest preffix that is also a suffix
     static void generateLPS(int lps[] , String p){
         int l = 0;
         int r = 1;
    
         while(l < p.length() && l < r && r < p.length()){
             if(p.charAt(l) == p.charAt(r)){
                 lps[r] = l + 1;
                 l++;
                 r++;
             }
             else{
                 if(l > 0)
                     l = lps[l - 1];
                 else
                     r++;    
             }
         }
     }
      
     // returns the index of the element which is just smaller than or
     // equal to the tar in the given arraylist 
     static int lowBound(ArrayList<Integer> ll,long tar ,int l,int r){
         if(l>r) return l;
 
         int mid=l+(r-l)/2;
 
         if(ll.get(mid)>=tar){
             return lowBound(ll,tar,l,mid-1);
         }
 
         return lowBound(ll,tar,mid+1,r);
     }
 
     // returns the index of the element which is just greater than or
     // equal to the tar in the given arraylist 
     static int upBound(ArrayList<Integer> ll,long tar,int l ,int r){
         if(l>r) return l;
 
         int mid=l+(r-l)/2;
 
         if(ll.get(mid)<=tar){
             return upBound(ll,tar,mid+1 ,r);
         }
 
         return upBound(ll,tar,l,mid-1);
     }
 
     static void swap(int a[] , int i , int j){
         int x = a[i];
         int y = a[j];
         a[j] = x;
         a[i] = y;
     }
     static void swap(long a[] , int i , int j){
         long x = a[i];
         long y = a[j];
         a[j] = x;
         a[i] = y;
    }
     // a -> z == 97 -> 122
 
     // String.format("%.9f", ans) ,--> to get upto 9 decimal places , (ans is double)
     
     // write 
 }
 