Problem: Max wants to buy a new skateboard. He has calculated the amount of money that is needed to buy a new skateboard. He left a calculator on the floor and went to ask some money from his parents. Meanwhile his little brother Yusuf came and started to press the keys randomly. Unfortunately Max has forgotten the number which he had calculated. The only thing he knows is that the number is divisible by 4.

You are given a string s consisting of digits (the number on the display of the calculator after Yusuf randomly pressed the keys). Your task is to find the number of substrings which are divisible by 4. A substring can start with a zero.

A substring of a string is a nonempty sequence of consecutive characters.

For example if string s is 124 then we have four substrings that are divisible by 4: 12, 4, 24 and 124. For the string 04 the answer is three: 0, 4, 04.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use gets/scanf/printf instead of getline/cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The only line contains string s (1 ≤ |s| ≤ 3·105). The string s contains only digits from 0 to 9.

Output

Print integer a — the number of substrings of the string s that are divisible by 4.

Note that the answer can be huge, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Examples

Input

124


Output

4


Input

04


Output

3


Input

5810438174


Output

9

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;
public class Codechef
{   static PrintWriter out=new PrintWriter(System.out);
	static FastScanner in = new FastScanner(System.in);
     static class FastScanner {BufferedReader br;StringTokenizer stok;FastScanner(InputStream is) {br = new BufferedReader(new InputStreamReader(is));}
        String next() throws IOException {while (stok == null || !stok.hasMoreTokens()) {String s = br.readLine();if (s == null) {return null;}
                stok = new StringTokenizer(s);}return stok.nextToken();}
        int ni() throws IOException {    return Integer.parseInt(next());}
        long nl() throws IOException {return Long.parseLong(next());}
        double nd() throws IOException {return Double.parseDouble(next());}
        char nc() throws IOException {return (char) (br.read());}
        String ns() throws IOException {return br.readLine();}
        int[] nia(int n) throws IOException{int a[] = new int[n];for (int i = 0; i < n; i++)a[i] = ni();return a;}
        long[] nla(int n) throws IOException {
            long a[] = new long[n];for (int i = 0; i < n; i++)a[i] = nl();return a;}
        double[] nda(int n)throws IOException {double a[] = new double[n];for (int i = 0; i < n; i++)        a[i] = nd();    return a;}
        int [][] imat(int n,int m) throws IOException
        {   int mat[][]=new int[n][m];for(int i=0;i<n;i++){   for(int j=0;j<m;j++)mat[i][j]=ni();}return mat;}
        
    }
        
    ///MAIN METHOD
    
    
    
    
	static long mod=Long.MAX_VALUE;
	public static void main (String[] args) throws java.lang.Exception
	{   int i,j;
	    HashMap<Integer,Integer> hm=new HashMap<Integer,Integer>();
		/*  if(hm.containsKey(z))
		        hm.put(z,hm.get(z)+1);
		    else
		        hm.put(z,1);
		 */       
        ArrayList<Integer> arr=new ArrayList<Integer>();
        HashSet<Integer> set=new HashSet<Integer>();
        PriorityQueue<Integer> pq=new PriorityQueue<Integer>();
        /*  int n = in.ni();
            int m = in.ni();
            String s=in.ns();
            int a[]=in.nia(n);
            int b[][]=in.im(n,m);
            pia(a);
		    pimat(b);
            sort(a,0,a.length-1);
        */
        String s=in.next();
        int n=s.length();
        long ans=0;
        for(i=1;i<n;i++)
        {
            int p=s.charAt(i)-'0';
            int q=s.charAt(i-1)-'0';
            //out.println("ending with="+q+p);
            //out.println("adding="+(i+1));
            int temp=p+10*q;
            if(temp%4==0)
                ans+=i;
        }
        //out.println("__"+ans);
        for(i=0;i<n;i++)
        {
            int p=s.charAt(i)-'0';
            if(p%4==0)
                ans++;
        }
        out.println(ans);
        out.close();
	}
	
	
	
	
	
	static long gcd(long a,long b)
	{   if(b==0)
	        return a;
	    return gcd(b,a%b);    
	}
	static long exponent(long a,long n)
	{   long ans=1;
	    while(n!=0)
	    {   if(n%2==1)
	            ans=(ans*a)%mod;
	       a=(a*a)%mod;
	       n=n>>1;
	    }
	    return ans;
	}
	static int binarySearch(int a[], int item, int low, int high) 
    {   if (high <= low) 
            return (item > a[low])?  (low + 1): low; 
        int mid = (low + high)/2; 
        if(item == a[mid]) 
            return mid+1; 
        if(item > a[mid]) 
            return binarySearch(a, item, mid+1, high); 
        return binarySearch(a, item, low, mid-1); 
    } 
   static void merge(int arr[], int l, int m, int r) 
    {   int n1 = m - l + 1; int n2 = r - m; int L[] = new int [n1]; int R[] = new int [n2]; 
        
        for (int i=0; i<n1; ++i) L[i] = arr[l + i]; for (int j=0; j<n2; ++j) R[j] = arr[m + 1+ j]; int i = 0, j = 0; int k = l; 
        while (i < n1 && j < n2) {   if (L[i] <= R[j]) {   arr[k] = L[i]; i++; } else{   arr[k] = R[j]; j++; } k++; } while (i < n1){   arr[k] = L[i]; i++; k++; } while (j < n2) { arr[k] = R[j];   j++;     k++; } 
    } 
    static void Sort(int arr[], int l, int r) 
    {    if (l < r) {   int m = (l+r)/2; Sort(arr, l, m); Sort(arr , m+1, r); merge(arr, l, m, r); } } 
    
    static void sort(int a[])
    {Sort(a,0,a.length-1);}

}