description: You are given an integer n. In 1 move, you can do one of the following actions:
  
    * erase any digit of the number (it's acceptable that the number before the operation has exactly one digit and after the operation, it is "empty"); 
    * add one digit to the right. 
  
  
  
  The actions may be performed in any order any number of times.
  
  Note that if, after deleting some digit from a number, it will contain leading zeroes, they will not be deleted. E.g. if you delete from the number 301 the digit 3, the result is the number 01 (not 1).
  
  You need to perform the minimum number of actions to make the number any power of 2 (i.e. there's an integer k (k ≥ 0) such that the resulting number is equal to 2^k). The resulting number must not have leading zeroes.
  
  E.g. consider n=1052. The answer is equal to 2. First, let's add to the right one digit 4 (the result will be 10524). Then let's erase the digit 5, so the result will be 1024 which is a power of 2.
  
  E.g. consider n=8888. The answer is equal to 3. Let's erase any of the digits 8 three times. The result will be 8 which is a power of 2.
  
  Input
  
  The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
  
  Each test case consists of one line containing one integer n (1 ≤ n ≤ 10^9).
  
  Output
  
  For each test case, output in a separate line one integer m — the minimum number of moves to transform the number into any power of 2.
  
  Example
  
  Input
  
  
  12
  1052
  8888
  6
  75
  128
  1
  301
  12048
  1504
  6656
  1000000000
  687194767
  
  
  Output
  
  
  2
  3
  1
  3
  0
  0
  2
  1
  3
  4
  9
  2
  
  Note
  
  The answer for the first test case was considered above.
  
  The answer for the second test case was considered above.
  
  In the third test case, it's enough to add to the right the digit 4 — the number 6 will turn into 64.
  
  In the fourth test case, let's add to the right the digit 8 and then erase 7 and 5 — the taken number will turn into 8.
  
  The numbers of the fifth and the sixth test cases are already powers of two so there's no need to make any move.
  
  In the seventh test case, you can delete first of all the digit 3 (the result is 01) and then the digit 0 (the result is 1).
solution: import java.io.*;
  import java.util.*;
  import java.math.BigDecimal;
  import java.math.*;
  
  public class Main{
  	public static void main(String[] args) {
  	    
  	      TaskA solver = new TaskA();
  	     
  		     
  	      int t = in.nextInt();
  	      for (int i = 1; i <= t ; i++) {
  	          solver.solve(i, in, out);
  	      }
  	     
  	      
  //	      solver.solve(1, in, out);
  	      
  	      
  	      out.flush();
  	    out.close();
  	  }
  	
  	 static class TaskA {
  	      public void solve(int testNumber, InputReader in, PrintWriter out) {
  	    	  int n=in.nextInt();
  	    	  long []pow=new long[60];
  	    	  pow[0]=1;
  	    	  for(int i=1;i<=59;i++) {
  	    		  pow[i]=2*pow[i-1];
  	    	  }
  	    	  
  	    	  int min=Integer.MAX_VALUE;
  	    	  
  	    	  for(int i=0;i<=59;i++) {
  	    		  int x=lpres(String.valueOf(n),String.valueOf(pow[i]),nD(n),nD(pow[i]));
  	    		 min=Math.min(nD(n)+nD(pow[i])-2*x,min);
  	    	  }
  	    	  println(min);
  	      }
  	  }
  	 
  	 static int nD(long num) {
  		 String s=String.valueOf(num);
  		 return s.length();
  	 }
  	 static int CommonDigits(int x,int y) {
  		 String s=String.valueOf(x);
  		 String s2=String.valueOf(y);
  		 return 0;
  	 }
  	 static int lpres(String str1,String str2,int m,int n) {
  		 int index=0;
  		 int length=0;
  		 for(int i=0;i<str1.length();i++) {
  			 if(index<str2.length() && str2.charAt(index)==str1.charAt(i)) {
  				 length++;
  				 index++;
  			 }
  		 }
  		 return length;
  	 }
  	 static int lcs(String str1, String str2, int m, int n)
  	    {
  	        int L[][] = new int[m + 1][n + 1];
  	        int i, j;
  	 
  	        // Following steps build L[m+1][n+1] in
  	        // bottom up fashion. Note that L[i][j]
  	        // contains length of LCS of str1[0..i-1]
  	        // and str2[0..j-1]
  	        for (i = 0; i <= m; i++) {
  	            for (j = 0; j <= n; j++) {
  	                if (i == 0 || j == 0)
  	                    L[i][j] = 0;
  	 
  	                else if (str1.charAt(i - 1)
  	                         == str2.charAt(j - 1))
  	                    L[i][j] = L[i - 1][j - 1] + 1;
  	 
  	                else
  	                    L[i][j] = Math.max(L[i - 1][j],
  	                                       L[i][j - 1]);
  	            }
  	        }
  	 
  	        // L[m][n] contains length of LCS
  	        // for X[0..n-1] and Y[0..m-1]
  	        return L[m][n];
  	    }
  	 class Pair 
  	 {
  	   int first ;int second  ;
  	  
  	   public  Pair(int x, int y)
  	   {
  	       this.first = x ;this.second = y ;
  	   }
  	 }
  	 boolean IsPowerOfTwo(int x)
  	 {
  	     return (x != 0) && ((x & (x - 1)) == 0);
  	 }
  	 
  	 static long power(long a,long b,long m ) {
  		 long ans=1;
  		 while(b>0) {
  			 if(b%2==1) {
  				 ans=((ans%m)*(a%m))%m; b--;
  			 }
  			 else {
  				 a=(a*a)%m;b/=2;
  			 }
  			 
  		 }
  		 return ans%m;
  	 }
  	 
  	 public static boolean repeatedSubString(String string) {
  		    return ((string + string).indexOf(string, 1) != string.length());
  		}
  	 static int search(char[]c,int start,int end,char x) {
  		 for(int i=start;i<end;i++) {
  			 if(c[i]==x) {return i;}
  		 }
  		 return -2;
  	 }
  	 
  	 static int bs(int size,int[]arr) {
  		 int x = -1;
      	 for (int b = size/2; b >= 1; b /= 2) {
          	 while (!ok(arr));
          	 }
      	 int k = x+1;
      	 return k;
  	 }
  	 
  	 static boolean ok(int[]x) {
  		 return false;
  	 }
  	 
  	 static int gcd(int a, int b) {
  	        while (b != 0) {
  	            int t = b;
  	            b = a % b;
  	            a = t;
  	        }
  	        return a;
  	    }
  	
  	 
  	
  	 
  	 static long fac(long a)
  	 {
  	     if(a== 0L || a==1L)return 1L ;
  	     
  	     return a*fac(a-1L) ;
  	 }
  	 
  	 
  	 
  	 static ArrayList al() {
  		 ArrayList<Integer>a =new ArrayList<>();
  			return a;
  		}
  	 
  	static HashSet h() {
  			return new HashSet<Integer>();
  		}
  	static void debug(int[][]a) {
  		int n= a.length;
  		for(int i=1;i<=n;i++) {
  	  		for(int j=1;j<=n;j++) {
  	  			out.print(a[i][j]+" ");
  	  		}
  	  		out.print("\n");
  	  	}
  	}
  	static void debug(int[]a) {
  			out.println(Arrays.toString(a));
  		}
  	
  	static void debug(ArrayList<Integer>a) {
  				out.println(a.toString());
  		}
  	
  	static boolean[]seive(int n){
  		boolean[]b=new boolean[n+1];
  		 for (int i = 2; i <= n; i++)
  	            b[i] = true;
  		 
  		for(int i=2;i*i<=n;i++) {
  			if(b[i]) {
  				for(int j=i*i;j<=n;j+=i) {
  					b[j]=false;
  				}
  			}
  		}
  		return b;
  	}
  	
  	 static int longestIncreasingSubseq(int[]arr) {
  		  int[]sizes=new int[arr.length];
  		  Arrays.fill(sizes, 1);
  		  int max=1;
  		  for(int i=1;i<arr.length;i++) {
  			  for(int j=0;j<i;j++) {
  				  if(arr[j]<arr[i]) {
  					  sizes[i]=Math.max(sizes[i],sizes[j]+1);
  					  max=Math.max(max, sizes[i]);
  				  }
  			  }
  		  }
  		  return max;
  	 }
  	 
  	 public static ArrayList primeFactors(long n)
  	    {
  		    ArrayList<Long>h= new ArrayList<>();
  	        // Print the number of 2s that divide n
  	        if(n%2 ==0) {h.add(2L);}
  	 
  	        // n must be odd at this point.  So we can
  	        // skip one element (Note i = i +2)
  	        for (long i = 3; i <= Math.sqrt(n); i+= 2)
  	        {
  	            if(n%i==0) {h.add(i);}
  	        }
  	        if (n > 2)
  	            h.add(n);
  	        return h;
  	    }
  	 
  	 static boolean Divisors(long n){
  		 if(n%2==1) {
  			 return true;
  		 }
  	     for (long i=2; i<=Math.sqrt(n); i++){
  	            if (n%i==0 && i%2==1){
  	                   return true;
  	            } 
  	        }
  	     return false;
  	    }
  	
  	static InputStream inputStream = System.in;
      static OutputStream outputStream = System.out;
      static InputReader in = new InputReader(inputStream);
      static PrintWriter out = new PrintWriter(outputStream);
      
      public static void superSet(int[]a,ArrayList<String>al,int i,String s) {
      	if(i==a.length) {
      		al.add(s);
      		return;
      	}
      	superSet(a,al,i+1,s);
      	superSet(a,al,i+1,s+a[i]+" ");
      }
      
  	public static long[] makeArr() {
  		long size=in.nextInt();
  		long []arr=new long[(int)size];
  		for(int i=0;i<size;i++) {
  			arr[i]=in.nextInt();
  		}
  		return arr;
  	}
  	
  	public static long[] arr(int n) {
  		long []arr=new long[n+1];
  		for(int i=1;i<n+1;i++) {
  			arr[i]=in.nextLong();
  		}
  		return arr;
  	}
  	
    public static void sort(long arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;
  
            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);
  
            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }
  
    static void print(int c) {
  		 out.print(c);
  	 }
  	 static void println(int x) {
  		 out.println(x);
  	 }
  	 static void print(String s) {
  		 out.print(s);
  	 }
  	 static void println(String s) {
  		 out.println(s);
  	 }
  public static void merge(long arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;
  
        /* Create temp arrays */
        long L[] = new long[n1];
        long R[] = new long[n2];
  
        //Copy data to temp arrays
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays
        int i = 0, j = 0;
  
        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
  
        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
  
        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
  
  public static void reverse(int[] array)
  {
      int n = array.length;
      for (int i = 0; i < n / 2; i++) {
          int temp = array[i];
          array[i] = array[n - i - 1];
          array[n - i - 1] = temp;
      }
  }
  
    public static long nCr(int n,int k)
    {
        long ans=1L;
        k=k>n-k?n-k:k;
       
        for( int j=1;j<=k;j++,n--)
        {
            if(n%j==0)
            {
                ans*=n/j;
            }else
            if(ans%j==0)
            {
                ans=ans/j*n;
            }else
            {
                ans=(ans*n)/j;
            }
        }
        return ans;
    }
    
    static int searchMax(int index,long[]inp) {
  	  while(index+1<inp.length &&inp[index+1]>inp[index]) {
  		  index+=1;
  	  }
  	  return index;
    }
    static int searchMin(int index,long[]inp) {
  	  while(index+1<inp.length &&inp[index+1]<inp[index]) {
  		  index+=1;
  	  }
  	  return index;
    }
  
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
  
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
  
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
  
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
      	  return Long.parseLong(next());
        }
    }
  }