Problem: Polycarp likes numbers that are divisible by 3.

He has a huge number s. Polycarp wants to cut from it the maximum number of numbers that are divisible by 3. To do this, he makes an arbitrary number of vertical cuts between pairs of adjacent digits. As a result, after m such cuts, there will be m+1 parts in total. Polycarp analyzes each of the obtained numbers and finds the number of those that are divisible by 3.

For example, if the original number is s=3121, then Polycarp can cut it into three parts with two cuts: 3|1|21. As a result, he will get two numbers that are divisible by 3.

Polycarp can make an arbitrary number of vertical cuts, where each cut is made between a pair of adjacent digits. The resulting numbers cannot contain extra leading zeroes (that is, the number can begin with 0 if and only if this number is exactly one character '0'). For example, 007, 01 and 00099 are not valid numbers, but 90, 0 and 10001 are valid.

What is the maximum number of numbers divisible by 3 that Polycarp can obtain?

Input

The first line of the input contains a positive integer s. The number of digits of the number s is between 1 and 2⋅10^5, inclusive. The first (leftmost) digit is not equal to 0.

Output

Print the maximum number of numbers divisible by 3 that Polycarp can get by making vertical cuts in the given number s.

Examples

Input

3121


Output

2


Input

6


Output

1


Input

1000000000000000000000000000000000


Output

33


Input

201920181


Output

4

Note

In the first example, an example set of optimal cuts on the number is 3|1|21.

In the second example, you do not need to make any cuts. The specified number 6 forms one number that is divisible by 3.

In the third example, cuts must be made between each pair of digits. As a result, Polycarp gets one digit 1 and 33 digits 0. Each of the 33 digits 0 forms a number that is divisible by 3.

In the fourth example, an example set of optimal cuts is 2|0|1|9|201|81. The numbers 0, 9, 201 and 81 are divisible by 3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.BigInteger;
import java.math.BigDecimal;
 
public class problem496_D {
   
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    
    void solve() throws IOException {
        String s = readString();
        int n = s.length();
        
        int r = 0;
        List<Integer> z = new ArrayList<Integer>();
        for (int i = 0; i < n+1; ++i) {
        	z.add(0);
        }
        int[] fin = new int[3];
        for (int i = 0; i < fin.length; ++i) {
        	fin[i] = -1;
        }
        fin[0] = 0;
        z.set(0, 0);
        
        for (int i = 1; i <= n; ++i) {
        	r = (r + s.charAt(i-1) - '0') % 3;
        	
        	z.set(i, z.get(i-1));
        	if (fin[r] != -1) {
        		z.set(i, max(z.get(i), z.get(fin[r])+1));
        	}
        	
        	fin[r] = i;
        }
        
        out.println(z.get(n));
    }
        
////////// Methods ///////////////////////////////////////////////////////////////////////////    

    int min(int... a) {
    	int min = Integer.MAX_VALUE;
    	
    	for (int i = 0; i < a.length; ++i) {
    		if (min > a[i]) {
    			min = a[i];
    		}
    	}
    	
    	return min;
    }
    
    int max(int... a) {
    	int max = Integer.MIN_VALUE;
    	
    	for (int i = 0; i < a.length; ++i) {
    		if (max < a[i]) {
    			max = a[i];
    		}
    	}
    	
    	return max;
    }
    
//////// #Methods //////////////////////////////////////////////////////////////////////////////////////////////////
    
/////// Classes //////////////////////////////////////////////////////////////////////////////////////////////////////////
    
    class Pair implements Comparable<Pair> {
    	long x;
    	long y;
    	
    	Pair() {
    		this.x = 0;
    		this.y = 0;
    	}
    	
    	Pair(long x, long y) {
    		this.x = x;
    		this.y = y;
    	}
    	
    	@Override
    	public boolean equals(Object obj) {
    		if (this == obj) {
    			return true;
    		}
    		if (obj == null) return false;
    		Pair other = (Pair) obj;
    		if (this.x == other.x && this.y == other.y) {
    			return true;
    		}
    		return false;
    	}
    	
    	@Override
    	public int compareTo(Pair other) {
    		if (this.x != other.x) return Long.compare(this.x, other.x);
    		return Long.compare(this.y*other.x, this.x*other.y);
    	}
    }
    
////// #Classes ////////////////////////////////////////////////////////////////////////////////////////////////////////////
    
/////// Initialization ////////////////////////////////////////////////////////////////////////////////////////////////////////
    
    public static void main(String[] args) {
        new problem496_D().run();
    }
   
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;
   
    void init() throws FileNotFoundException {
      
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("D:\\Java-programs\\eclipse-workspace\\OLYMP\\src\\input.txt"));
            out = new PrintWriter("D:\\Java-programs\\eclipse-workspace\\OLYMP\\src\\output.txt");
        }
       
        tok = new StringTokenizer("");
    }
   
    void run() {
        try {
            long timeStart = System.currentTimeMillis();
           
            init();
            solve();
           
            out.close();
           
            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeStart));
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }
   
    String readLine() throws IOException {
        return in.readLine();
    }
   
    String delimiter = " ";
   
    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;
           
            tok = new StringTokenizer(nextLine);
        }
       
        return tok.nextToken(delimiter);
    }
   
    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
   
    long readLong() throws IOException {
        return Long.parseLong(readString());
    }
    
    double readDouble() throws IOException {
    	return Double.parseDouble(readString());
    }       
}

////////// #Initialization //////////////////////////////////////////////////////////////////////////////////////