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:
   // package com.company;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.lang.reflect.Array;
    import java.sql.SQLOutput;
    import java.util.*;
    public class Main {

        public static void main(String[] args) throws IOException {
           Scanner s = new Scanner(System.in);
//   BufferedReader s=new BufferedReader(new InputStreamReader(System.in));
              StringBuilder sb = new StringBuilder();//int n=Integer.parseInt(s.readLine());
        char[] a=s.next().toCharArray();int ans=0;int i=0;
        for( i=0;i<a.length-1;i++){
            if((a[i]-48)%3==0) ans++;
            else if((a[i]-48+a[i+1]-48)%3==0) {ans++;i+=1;}
            else if((a[i+1]-48)%3==0){
    ans++;i+=1;
            }
               else if(i+2<a.length&&(a[i]-48+a[i+1]-48+a[i+2]-48)%3==0) {
                ans++;i+=2;
            }
        }if(i==a.length-1&&a[i]%3==0) ans++;
            System.out.println(ans);
        }
        static  void computeLPSArray(String pat, int M, int lps[])
        {
            int len = 0;
            int i = 1;
            lps[0] = 0;
            while (i < M) {
                if (pat.charAt(i) == pat.charAt(len)) {
                    len++;
                    lps[i] = len;
                    i++;
                }
                else // (pat[i] != pat[len])
                {
                    if (len != 0) {
                        len = lps[len - 1];
   }
                    else // if (len == 0)
                    {
                        lps[i] = len;
                        i++;
                    }
                }
            }
        }
        static boolean isPrime(int n)
        {
            // Corner cas
            if (n <= 1) return false;
            if (n <= 3) return true;

            // This is checked so that we can skip
            // middle five numbers in below loop
            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 boolean isPrime(int n, int k)
        {
            // Corner cases
            if (n <= 1 || n == 4) return false;
            if (n <= 3) return true;

            // Try k times
            while (k > 0)
            {
                // Pick a random number in [2..n-2]
                // Above corner cases make sure that n > 4
                int a = 2 + (int)(Math.random() % (n - 4));

                // Fermat's little theorem
                if (power(a, n - 1, n) != 1)
                    return false;

                k--;
            }

            return true;
        }
        static double power(double x, long y, int p) {
            double res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }
        public static void fracion(double x) {
            String a = "" + x;
            String spilts[] = a.split("\\."); // split using decimal
            int b = spilts[1].length(); // find the decimal length
            int denominator = (int) Math.pow(10, b); // calculate the denominator
            int numerator = (int) (x * denominator); // calculate the nerumrator Ex
            // 1.2*10 = 12
            int gcd = (int)gcd((long)numerator, denominator); // Find the greatest common
            // divisor bw them
            String fraction = "" + numerator / gcd + "/" + denominator / gcd;
            // System.out.println((denominator/gcd));
            long x1=modInverse(denominator / gcd,998244353  );
            //  System.out.println(x1);
            System.out.println((((numerator / gcd )%998244353 *(x1%998244353  ))%998244353  ) );
        }static int max=Integer.MIN_VALUE;
static int max1=Integer.MIN_VALUE;static long[][] dp;static int[][] c;static int k=1;static int bhoo=0;
static int[] car;static int ans;static HashMap<Integer,Integer>[] ha;
public static void dfs(int ans2,int papa, int i, ArrayList<Integer>[] h, int[] vis,HashMap<Integer,Integer>[] bad) {
    vis[i] = 1;
    if(i!=1&&h[i].size()==1){
    if(ans2!=-1)  {ans++;  sb1.append(ans2+" ");}
    }
    if(h[i]==null) return;
int hu=0;int hai=0;
for(Integer j:h[i]){
    if(vis[j]==0&&bad[i].containsKey(j)) {
        hai=1;break;
    }
}int khi=0;
             for(Integer j:h[i]) {//if(vis[j]==0) flag=1;
                    if(vis[j]==0){
                        if(!bad[i].containsKey(j)){
                        if(hai==0&&khi==0){khi=1;    dfs(ans2,papa,j,h,vis,bad);}
                        else dfs(-1,papa,j,h,vis,bad);
                        }else{
                            if(hu==0){
                                if(papa==0){//ans++;//sb1.append(j+" ");
                                    dfs(j,1,j,h,vis,bad);
                                }else{
                                hu=1;
                                dfs( j,1,j,h,vis,bad);}
                            }else{
                            //    ans++;//sb1.append(j+" ");
                                dfs(j,1,j,h,vis,bad);
                            }
                        }
                    }
             }//if(flag==1) bhoo=-1;
        }static StringBuilder sb1=new StringBuilder();
        public static void bfs(int i, HashMap<Integer, Integer>[] h, int[] vis, int len, int papa) {
            Queue<Integer> q = new LinkedList<Integer>();
            q.add(i);
   }
      static int i(String a) {
            return Integer.parseInt(a);
        }
     static long l(String a) {
            return Long.parseLong(a);
        }
        static String[] inp() throws IOException {
            BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
            return s.readLine().trim().split("\\s+");
        }


        static long gcd(long a, long b) {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }
        static long modInverse(int a, int m)
        {


            {
                // 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(int x, int y, int 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;
        }

        // Function to return gcd of a and b

    }
    class Student
    {
        int l;int r;int i;
        public Student(int l, int r,int i) {
            this.l = l;
            this.r = r;this.i=i;
        }
    // Constructor


        // Used to print student details in main()
        public String toString()
        {
            return this.l+" ";
        }
    }

    class Sortbyroll implements Comparator<Student>
    {
        // Used for sorting in ascending order of
        // roll number
        public int compare(Student a, Student b){
      return a.l-b.l;  }
    } class Sortbyroll1 implements Comparator<Student>
    {
        // Used for sorting in ascending order of
        // roll number
        public int compare(Student a, Student b){
        return a.l-b.l;
        }
    }