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.BigInteger;
  
  /**
   __                  __
   ( _)                ( _)
   / / \\              / /\_\_
   / /   \\            / / | \ \
   / /     \\          / /  |\ \ \
   /  /   ,  \ ,       / /   /|  \ \
   /  /    |\_ /|      / /   / \   \_\
   /  /  |\/ _ '_| \   / /   /   \    \\
   |  /   |/  0 \0\    / |    |    \    \\
   |    |\|      \_\_ /  /    |     \    \\
   |  | |/    \.\ o\o)  /      \     |    \\
   \    |     /\\`v-v  /        |    |     \\
   | \/    /_| \\_|  /         |    | \    \\
   | |    /__/_ `-` /   _____  |    |  \    \\
   \|    [__]  \_/  |_________  \   |   \    ()
   /    [___] (    \         \  |\ |   |   //
   |    [___]                  |\| \|   /  |/
   /|    [____]                  \  |/\ / / ||
   (  \   [____ /     ) _\      \  \    \| | ||
   \  \  [_____|    / /     __/    \   / / //
   |   \ [_____/   / /        \    |   \/ //
   |   /  '----|   /=\____   _/    |   / //
   __ /  /        |  /   ___/  _/\    \  | ||
   (/-(/-\)       /   \  (/\/\)/  |    /  | /
   (/\/\)           /   /   //
   _________/   /    /
   \____________/    (
  
  
   @author NTUDragons-Reborn
   */
  
  public class Solution{
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          Task solver = new Task();
          solver.solve(in, out);
          out.close();
      }
      // main solver
      static class Task{
  
          double eps= 0.00000001;
          static final int MAXN = 1010;
          static final int MOD= 1000000007;
  
          // stores smallest prime factor for every number
          static int spf[] = new int[MAXN];
  
          static boolean[] prime;
  
          Map<Integer,Set<Integer>> dp= new HashMap<>();
  
          // Calculating SPF (Smallest Prime Factor) for every
          // number till MAXN.
          // Time Complexity : O(nloglogn)
          public void sieve()
          {
              spf[1] = 1;
              for (int i=2; i<MAXN; i++)
  
                  // marking smallest prime factor for every
                  // number to be itself.
                  spf[i] = i;
  
              // separately marking spf for every even
              // number as 2
              for (int i=4; i<MAXN; i+=2)
                  spf[i] = 2;
  
              for (int i=3; i*i<MAXN; i++)
              {
                  // checking if i is prime
                  if (spf[i] == i)
                  {
                      // marking SPF for all numbers divisible by i
                      for (int j=i*i; j<MAXN; j+=i)
  
                          // marking spf[j] if it is not
                          // previously marked
                          if (spf[j]==j)
                              spf[j] = i;
                  }
              }
          }
  
          void sieveOfEratosthenes(int n)
          {
              // Create a boolean array
              // "prime[0..n]" and
              // initialize all entries
              // it as true. A value in
              // prime[i] will finally be
              // false if i is Not a
              // prime, else true.
              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] is not changed, then it is a
                  // prime
                  if (prime[p] == true)
                  {
                      // Update all multiples of p
                      for (int i = p * p; i <= n; i += p)
                          prime[i] = false;
                  }
              }
          }
  
          // A O(log n) function returning primefactorization
          // by dividing by smallest prime factor at every step
          public Set<Integer> getFactorization(int x)
          {
              if(dp.containsKey(x)) return dp.get(x);
              Set<Integer> ret = new HashSet<>();
              while (x != 1)
              {
                  if(spf[x]!=2) ret.add(spf[x]);
                  x = x / spf[x];
              }
              dp.put(x,ret);
              return ret;
          }
          // function to find first index >= x
          public int lowerIndex(List<Integer> arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
          public int lowerIndex(int[] arr, int n, int x)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] >= x)
                      h = mid - 1;
                  else
                      l = mid + 1;
              }
              return l;
          }
  
          // function to find last index <= y
          public int upperIndex(List<Integer> arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr.get(mid) <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
          public int upperIndex(int[] arr, int n, int y)
          {
              int l = 0, h = n - 1;
              while (l <= h)
              {
                  int mid = (l + h) / 2;
                  if (arr[mid] <= y)
                      l = mid + 1;
                  else
                      h = mid - 1;
              }
              return h;
          }
  
          // function to count elements within given range
          public int countInRange(List<Integer> arr, int n, int x, int y)
          {
              // initialize result
              int count = 0;
              count = upperIndex(arr, n, y) -
                      lowerIndex(arr, n, x) + 1;
              return count;
          }
  
          public int add(int a, int b){
              a+=b;
              if(a>=MOD) a-=MOD;
              else if(a<0) a+=MOD;
              return a;
          }
  
          public int mul(int a, int b){
              long res= (long)a*(long)b;
              return (int)(res%MOD);
          }
  
          public int power(int a, int b) {
              int ans=1;
              while(b>0){
                  if((b&1)!=0) ans= mul(ans,a);
                  b>>=1;
                  a= mul(a,a);
              }
              return ans;
          }
  
          int[] fact= new int[MAXN];
          int[] inv= new int[MAXN];
  
          public int Ckn(int n, int k){
              if(k<0 || n<0) return 0;
              return mul(mul(fact[n],inv[k]),inv[n-k]);
          }
  
          public int inverse(int a){
              return power(a,MOD-2);
          }
  
          public void preprocess() {
              fact[0]=1;
              for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
              inv[MAXN-1]= inverse(fact[MAXN-1]);
              for(int i=MAXN-2;i>=0;i--){
                  inv[i]= mul(inv[i+1],i+1);
              }
          }
  
          /**
           * return VALUE of lower bound for unsorted array
           */
          public int lowerBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.lower(x);
          }
          /**
           * return VALUE of upper bound for unsorted array
           */
          public int upperBoundNormalArray(int[] arr, int x){
              TreeSet<Integer> set= new TreeSet<>();
              for(int num: arr) set.add(num);
              return set.higher(x);
          }
  
          public void debugArr(int[] arr){
              for(int i: arr) out.print(i+" ");
              out.println();
          }
  
          public int rand(){
              int min=0, max= MAXN;
              int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
              return random_int;
          }
          
          InputReader in; PrintWriter out;
          
          public void solve(InputReader in, PrintWriter out) {
              this.in=in; this.out=out;
              int t=in.nextInt();
              while(t-->0){
                  solveC();
              }
          }
  
          public void solveC(){
              int n= in.nextInt();
              int res=Integer.MAX_VALUE;
              // long val=0;
              for(int z=0;z<=60;z++){
                  long target= (long)Math.pow(2,z);
                  char[] num= (n+"").toCharArray();
                  char[] tar= (target+"").toCharArray();
                  int i=0,j=0;
                  for(;i<num.length;i++){
                      if(j>=tar.length) break;
                      if(num[i]==tar[j])j++;
                  }
                  res= Math.min(res,num.length-j+tar.length-j);
              }
              out.println(res);
          }
      }
  
      static class DSU {
          int[] par;
          int n;
          int[] rank;
          
          public DSU(int n){
              this.n= n;
              this.par= new int[n+1];
              for(int i=1;i<=n;i++) par[i]=i;
              this.rank= new int[n+1];
              Arrays.fill(rank,1);
          }
          public int find(int u){
              if(par[u]==u) return u;
              par[u]= find(par[u]);
              return par[u];
          }
          public void merge(int u, int v){
              u= find(u); v= find(v);
              if(u!=v){
                  if(rank[u]>rank[v]){
                      int temp=u; u= v;v= temp;
                  }
                  par[u]= v;
                  rank[v]+=rank[u];
              }
          } 
          public boolean already(int u, int v){
              if(find(u)==find(v)) return true;
              return false;
          }
      }
  
      static class SEG {
          public long _gcd(long a,  long  b)
          {
  
              if(b == 0) {
                  return a;
              }
              else {
                  return _gcd(b, a % b);
              }
          }
          long[] segs;
          public SEG(List<Long> a) {
              int n= a.size();
              segs= new long[4*n];
              build(0,a,0,n-1);
          }
          void build(int root, List<Long> a, int l, int r){
              if (l==r){
                  segs[root] = a.get(l); return;
              }
              int m = (l+r) >> 1;
              build(root*2+1, a, l, m);
              build(root*2+2, a, m+1, r);
              segs[root] = _gcd(segs[root*2+1], segs[root*2+2]);
          }
          long query(int root, int l, int r, int lq, int rq){
              if (lq > r || rq < l) return 0l;
              if (l >= lq && rq >= r) return segs[root];
              int m = (l+r)>>1;
              return _gcd(query(root*2+1, l, m, lq, rq),
                           query(root*2+2, m+1, r, lq, rq));
          }
      }
  
      static class Venice{
          public Map<Long,Long> m= new HashMap<>();
          public long base=0;
          public long totalValue=0;
          private int M= 1000000007;
  
          private long addMod(long a, long b){
              a+=b;
              if(a>=M) a-=M;
              return a;
          }
  
          public void reset(){
              m= new HashMap<>();
              base=0;
              totalValue=0;
          }
          public void update(long add){
              base= base+ add;
          }
          public void add(long key, long val){
              long newKey= key-base;
              m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
          }
      }
  
  
  
      static class Tuple implements Comparable<Tuple>{
          int x, y, z;
          public Tuple(int x, int y, int z){
              this.x= x;
              this.y= y;
              this.z=z;
          }
          @Override
          public int compareTo(Tuple o){
              return this.z-o.z;
          }
      }
  
      static class Pair implements Comparable<Pair>{
          public int x;
          public int y;
          public Pair(int x, int y){
              this.x= x;
              this.y= y;
          }
  
          @Override
          public int compareTo(Pair o) {
              return this.x-o.x;
          }
      }
  
      // public static class compareL implements Comparator<Tuple>{
      //     @Override
      //     public int compare(Tuple t1, Tuple t2) {
      //         return t2.l - t1.l;
      //     }
      // }
  
      // fast input reader class;
      static class InputReader {
          BufferedReader br;
          StringTokenizer st;
  
          public InputReader(InputStream stream) {
              br = new BufferedReader(new InputStreamReader(stream));
          }
  
          public String nextToken() {
              while (st == null || !st.hasMoreTokens()) {
                  String line = null;
                  try {
                      line = br.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
                  if (line == null) {
                      return null;
                  }
                  st = new StringTokenizer(line);
              }
              return st.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(nextToken());
          }
          public double nextDouble(){
              return Double.parseDouble(nextToken());
          }
          public long nextLong(){
              return Long.parseLong(nextToken());
          }
          public int[] nextIntArr(int n){
              int[] arr= new int[n];
              for(int i=0;i<n;i++) arr[i]= nextInt();
              return arr;
          }
          public long[] nextLongArr(int n){
              long[] arr= new long[n];
              for(int i=0;i<n;i++) arr[i]= nextLong();
              return arr;
          }
          public List<Integer> nextIntList(int n){
              List<Integer> arr= new ArrayList<>();
              for(int i=0;i<n;i++) arr.add(nextInt());
              return arr;
          }
          public int[][] nextIntMatArr(int n, int m){
              int[][] mat= new int[n][m];
              for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
              return mat;
          }
          public List<List<Integer>> nextIntMatList(int n, int m){
              List<List<Integer>> mat= new ArrayList<>();
              for(int i=0;i<n;i++){
                  List<Integer> temp= new ArrayList<>();
                  for(int j=0;j<m;j++) temp.add(nextInt());
                  mat.add(temp);
              }
              return mat;
          }
          public char[] nextStringCharArr(){
              return nextToken().toCharArray();
          }
      }
  }