In the city of Saint Petersburg, a day lasts for 2^{100} minutes. From the main station of Saint Petersburg, a train departs after 1 minute, 4 minutes, 16 minutes, and so on; in other words, the train departs at time 4^k for each integer k ≥ 0. Team BowWow has arrived at the station at the time s and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time s. For example if s = 20, then they missed trains which have departed at 1, 4 and 16. As you are the only one who knows the time, help them!

Note that the number s will be given you in a [binary representation](https://en.wikipedia.org/wiki/Binary_number#Representation) without leading zeroes.

Input

The first line contains a single binary number s (0 ≤ s < 2^{100}) without leading zeroes.

Output

Output a single number — the number of trains which have departed strictly before the time s.

Examples

Input


100000000


Output


4


Input


101


Output


2


Input


10100


Output


3

Note

In the first example 100000000_2 = 256_{10}, missed trains have departed at 1, 4, 16 and 64.

In the second example 101_2 = 5_{10}, trains have departed at 1 and 4.

The third example is explained in the statements.
import java.io.*; 
import java.util.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class untitled 
{ 
  //  static int n;static ArrayList<Integer> arr[];
   // int ans[];
    public static void main(String[] args) throws IOException { 
    //    Scanner sc=new Scanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        br = new BufferedReader(new InputStreamReader(System.in));
        String n=next();
        //int a=Integer.parseInt(n);
        int len=n.length();
        int check=0;
        for(int i=1;i<len;i++){
            if(n.charAt(i)=='1'){
                check=1;
                break;
            }
        }
        if(len%2==0){
            pw.println(len/2);
        }
        else{
            if(check==1){
                pw.println((len/2)+1);
            }
            else{
                pw.println(len/2);
            }
        }
        pw.close();
    }
   
    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
 
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    static class Pair{
        int x;int y;
        Pair(int x,int y){
            this.x=x;
            this.y=y;
          //  this.i=i;
        }
    }
    static class sorting implements Comparator<Pair>{
        public int compare(Pair a,Pair b){
            //return (a.y)-(b.y);
            return (a.x-b.x);
        }
    }
    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  
            n % 3 == 0) 
            return false; 
      
        for (int i = 5; 
                 i * i <= n; i = i + 6) 
            if (n % i == 0 || 
                n % (i + 2) == 0) 
                return false; 
      
        return true; 
    } 
    static long gcd(long a, long b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }  
    static long modInverse(long a, long m) { 
        long g = gcd(a, m); 
        if (g != 1) 
            return -1; 
        else{ 
            // If a and m are relatively prime, then modulo inverse 
            // is a^(m-2) mode m 
            return (power(a, m - 2, m)); 
        } 
    } 
      
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
       static long modInverse(long n,int M){
        return fast_pow(n,M-2,M);
    }
    
} 