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.io.*;
import java.math.*;
import java.math.BigInteger;
import java.text.DecimalFormat;
 public class Tester {
	//static long sum=0,sum1=Long.MAX_VALUE;
	//DecimalFormat df = new DecimalFormat("#.#####");
	public static final int MOD = (int) (1e9 + 7);
	public static void main(String args[])
	{
		InputReader in = new InputReader(System.in);
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		long n,count=0,i;
		String s=in.next();
		n=s.length();
		for(i=0;i<n;i++)
		{
			if((s.charAt((int)i)-'0')%4==0)
			{
				count++;
			}
		}
		for(i=0;i<n-1;i++)
		{
			if(((s.charAt((int)i)-'0')*10+(s.charAt((int)(i+1))-'0'))%4==0)
			{
				count+=(i+1);	
			}
		}
		out.println(count);
		out.close();
	}
	private static int[] nextIntArray(InputReader in,int n)	
	{
		int[] a=new int[n];
		for(int i=0;i<n;i++)
			a[i]=in.nextInt();
		return a;
	}
	public static double dis(double x1,double x2,double y1)
	{
		return Math.sqrt(((x1-x2)*(x1-x2))+(y1*y1));
	}
	private static String[] nextStringArray(InputReader in,int n)	
	{
		String[] a=new String[n];
		for(int i=0;i<n;i++)
			a[i]=in.next();
		return a;
	}
	private static void show(int[] a)
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
	}
	private static void show2DArray(char[][] a)
	{
		for(int i=0;i<a.length;i++)
		{
			for(int j=0;j<a[0].length;j++)
				System.out.print(a[i][j]);
			System.out.println();
		}
	}
 static long fact(long x)
 {
	 long i=x,mul=1;
	 while(i>0)
	 {
		 mul=(mul%1000000007)*(i%1000000007)%1000000007;
		 i--;
	 }
	 return mul;
 }
 static class LengthComparator implements Comparator<String> {
	    public int compare(String arg0, String arg1) {
		// Use Integer.compare to compare the two Strings' lengths.
		return (arg0+arg1).compareTo(arg1+arg0);
	    }
	}
// static long output(ArrayList<Integer> h[],int j,boolean[] v)
// {
//	 int k;
//	 v[j]=true;
//	 sum++;
//	 for(k=0;k<h[j].size();k++)
//	 {
//		 if(v[h[j].get(k)]==false)
//		 {
//			 output(h,h[j].get(k),v);
//		 }
//	 }
//	 return sum;
// }
 static long func(boolean v[],int j,ArrayList<Integer> h[],long ban[])
 {
	 	v[j]=true;
	 	 int k;
	 	long sum=0;
	    sum=sum+ban[j];
	 	//System.out.println(h[j].size());
	 	for(k=0;k<h[j].size();k++)
	 	{
	 		if(v[h[j].get(k)]==false)
	 		{
	 			v[h[j].get(k)]=true;
	 			sum+=func(v,h[j].get(k),h,ban);
	 		}
	 	}
	 	return sum;
 }
/*static class Graph {
    	
    	private static Deque<Integer> stack = new ArrayDeque<Integer>();
 		private int least,count,v;
 		
		Set<Integer>[] cities;
    	private int[] risk;
    	
    	Graph(int n,String[] risk){
    		
    		cities = new HashSet[n];
    		this.risk = new int[n];
    		for(int i =0;i<n;i++){
    			cities[i] = new HashSet<>();
    		}
    		for(int i =0;i<n;i++){
    			this.risk[i] = Integer.parseInt(risk[i]);
    		}
    		visited = new boolean[n];
    	}
    	
    	
    	public void add(int x,int y){
    		cities[x].add(y);
    		cities[y].add(x);
    	}
}*/
	static int root(int arr[],int i)
	{
		while(arr[i]!=i)
		{
			i=arr[i];
		}
		return i;
	}
	static boolean find(int arr[],int a,int b)
	{
		if(root(arr,a)==root(arr,b))
		{
			return true;
		}
		else
			return false;
	}
	static void weighted_union(int arr[],int size[],int a,int b)
	{
		int root_a=root(arr,a);
		int root_b=root(arr,b);
		if(root_a!=root_b)
		{
			if(size[root_a]<size[root_b])
			{
				arr[root_a]=arr[root_b];
				size[root_b]+=size[root_a];
			}
			else
			{
				arr[root_b]=arr[root_a];
				size[root_a]+=size[root_b];
			}
		//	count--;
		}
	}
	static class Pair implements Comparable<Pair>
	{
		private long first;
		private long index;
		//private long second;;

		public Pair(long i, long j) 
		{ 
			this.first = i;
			this.index = j;
		}
		public long getFirst() { return first; }
		//public long getSecond() { return second; }
		public long getIndex() { return index ;}
		public void setFirst(long k) { this.first=k ; }
		public void setIndex(long k) { this.index=k ;}
		//public void setSecond(long k) { this.second=k ;}
		@Override
		public int compareTo(Pair o) 
		{
			return Long.compare(this.first, o.first);
		}
	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) {
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine(){
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}