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.util.*;
import java.io.*;

public class virtual1{

    static InputReader in = new InputReader();
    static PrintWriter out = new PrintWriter(System.out);
    
    static void randomShuffle(String ar[]){
		int l = ar.length;
		Random rd = new Random();
		int cnt = 50;
		while(cnt-->0){
			int n1 = rd.nextInt(l);
			int n2 = rd.nextInt(l);
			String temp = ar[n1];
			ar[n1] = ar[n2];
			ar[n2] = temp;
		}

    }
    public static void mergeSort(int ar[],int start,int end){
        if(start>=end)
        return;

        int mid = (start+end)/2;

        mergeSort(ar, start, mid);
        mergeSort(ar, mid+1, end);
        merge(ar,start,mid,end);
    }
    public static void merge(int ar[],int start,int mid,int end){
        int l[] = new int[mid-start+1];
        int r[] = new int[end - mid];

        int inx = start;
        int i =0;
        while(inx<=mid){
            l[i++]=ar[inx++];
        }
        i = 0;
        while(inx<=end){
            r[i++]=ar[inx++];
        }
        int p1 = 0;
        int l1 = l.length;
        int p2 = 0;
        int l2 = r.length;

        for(i=start;i<=end;i++){
            if(p1<l1&&p2<l2){
                if(l[p1]<=r[p2]){
                    ar[i]=l[p1++];
                }
                else{
                    ar[i]=r[p2++];
                }
            }
            else if(p1<l1){
                ar[i]=l[p1++];
            }
            else{
                ar[i]=r[p2++];
            }
        }
    }

    public static void quickSort(int ar[], int start, int end){
        if(start<end){
            int pi = partition1(ar,start,end);

            quickSort(ar, start, pi-1);
            quickSort(ar,pi+1,end);
        }
    }

    public static int partition1(int ar[],int start,int end){
        int pi = start;
        int ele = ar[start];
        int inx = -1;
        for(int i=start+1;i<=end;i++){
            if(ar[i]<ele){
                int temp = ar[pi];
                ar[pi] = ar[i];
                ar[i] = temp;
                inx = i;
                pi++;
            }
        }
        if(inx!=-1){
            int temp = ar[pi];
            ar[pi] = ar[inx];
            ar[inx] = temp;
        }
        return pi;
    }
    public static int partition2(int ar[],int start,int end){
        int pi = start;
        int ele = ar[end];
        for(int i=start;i<end;i++){
            if(ar[i]<ele){
                int temp = ar[pi];
                ar[pi] = ar[i];
                ar[i] = temp;
                pi++;
            }
        }
        int temp = ar[pi];
        ar[pi] = ar[end];
        ar[end] = temp;
        return pi;
    }
    public static void main(String[] args) {
        String s = in.nextLine();
        char ar[] = s.toCharArray();
        int n =s.length();
        int ans = 0;
        int cnt = 0;
        Queue<Integer>st = new LinkedList<>();
        for(int i=0;i<n;i++){
            int x = ar[i]-'0';
            st.add(x);
            cnt+=x;
            if(cnt%3==0&&!st.isEmpty()){
                //out.println(i+" A");
                ans++;
                st.clear();
            }
            if(x%3==0&&!st.isEmpty()){
                //out.println(i+" B");
                ans++;
                st.clear();
                cnt =0;
            }
            if(st.size()==3){
                cnt-=st.poll();
                if(cnt%3==0){
                    //out.println(i+" C");
                    ans++;
                    st.clear();
                    cnt = 0;
                }
            }
        }
        out.println(ans);
        out.close();    
    }

    static void debug(Object ...o){
        System.out.println(Arrays.deepToString(o));
    }
    static class InputReader{
        BufferedReader br;
        StringTokenizer st;
 
        public InputReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}