A binary string is a string that consists of characters 0 and 1.

Let \operatorname{MEX} of a binary string be the smallest digit among 0, 1, or 2 that does not occur in the string. For example, \operatorname{MEX} of 001011 is 2, because 0 and 1 occur in the string at least once, \operatorname{MEX} of 1111 is 0, because 0 and 2 do not occur in the string and 0 < 2.

A binary string s is given. You should cut it into any number of substrings such that each character is in exactly one substring. It is possible to cut the string into a single substring — the whole string.

A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

What is the minimal sum of \operatorname{MEX} of all substrings pieces can be?

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

Each test case contains a single binary string s (1 ≤ |s| ≤ 10^5).

It's guaranteed that the sum of lengths of s over all test cases does not exceed 10^5.

Output

For each test case print a single integer — the minimal sum of \operatorname{MEX} of all substrings that it is possible to get by cutting s optimally.

Example

Input


6
01
1111
01100
101
0000
01010


Output


1
0
2
1
1
2

Note

In the first test case the minimal sum is \operatorname{MEX}(0) + \operatorname{MEX}(1) = 1 + 0 = 1.

In the second test case the minimal sum is \operatorname{MEX}(1111) = 0.

In the third test case the minimal sum is \operatorname{MEX}(01100) = 2.
import java.util.*;
public class MyClass {
    
    public static int getLength(String str)
    {
        int n=str.length();
        if(n>0)
        return n;
        else
        return 0;
    }
    public static void reddyAns(int a,int b)
    {
        if(a<=2)
          System.out.println(a);
        else if(a<0)
          System.out.println("-1");
        else if(b==0)
          System.out.println("1");
        else if(a==0)
          System.out.println("0");
        else if(b<0)
          System.out.println("-8");
        else
          System.out.println("2");
    }
    
    public static boolean checkFRE(int k)
    {
        if(k>0)
        return true;
        else
        return false;
    }
    
    public static int hadi(int z)
    {
        int e=z+1;
        return e;
    }
    
    public static int buzzi(int l)
    {
        int r=l+1;
        return r;
    }
    
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      int t=sc.nextInt();
      int x,y,z,kii;
      String str;
      for(int i=0;i<t;i++)
      {
          str=sc.next();
          int yeshw=9;
          int reddy=7;
          z=yeshw-reddy;
          z=2;
          x=0;
          y=0;
          int kit=0;
          int n=getLength(str);
          for(int yesh=0;yesh<n;yesh++)
          {
              char ch=str.charAt(yesh);
              if(ch!=z)
              {
                  if(ch=='1'){
                    y=hadi(y);
                  }
                  else if(ch!='0' && ch!='1')
                  kit++;
                  else{
                      x=buzzi(x);
                  }
                  z=ch;
                  kit++;
                  boolean fi=checkFRE(kit);
                  if(!fi)
                  {
                      break;
                  }
              }
              for(int o=0;o<1;o++)
              {
                  break;
              }
              
          }
          reddyAns(x,y);
          
      }
    }
}