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.*;
	public class Main {
		public static long mod= (long) (1e9 +7);
		static int kill[],sum[];
		static int n;
		static Pair p[];
		public static void main(String args[])
		{
			InputReader s= new InputReader(System.in);
			OutputStream outputStream= System.out;
			PrintWriter out= new PrintWriter(outputStream);
			String st= s.next();
			long cnt=0;
			int n= st.length();
			for(int i=0;i<n;i++){
				if((st.charAt(i)-'0')%4==0)
					cnt++;
			}
			
			for(int i=1;i<n;i++){
				if(Integer.parseInt(st.substring(i-1, i+1))%4==0){
					cnt+=i;
				}
			}
			out.println(cnt);
			out.close();
		}
		
		static long combinations(long n,long r){   // O(r)
			if(r==0 || r==n) return 1;
			r= Math.min(r, n-r);
			long ans=n;  // nC1=n;
			for(int i=1;i<r;i++){
				ans= ans*(n-i);
				ans= ans/(i+1);
			}
			return ans;
			
		}
		public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
		static void catalan_numbers(int n) {
			long catalan[]= new long[n+1];
		    catalan[1] = 1;
		    for (int i = 2; i <= n; i++) {
		        for (int j = 1; j <= i - 1; j++) {
		            catalan[i] = catalan[i] + ((catalan[j]) * catalan[i - j]);
		        }
		    }
		}
		
		static ArrayList<Integer> primeFactors(int n)   // O(sqrt(n))
		{
		    // Print the number of 2s that divide n
			ArrayList<Integer> arr= new ArrayList<>();
		    while (n%2 == 0)
		    {
		        arr.add(2);
		        n = n/2;
		    }
		 
		    // n must be odd at this point.  So we can skip one element (Note i = i +2)
		    for (int i = 3; i <= Math.sqrt(n); i = i+2)
		    {
		        // While i divides n, print i and divide n
		        while (n%i == 0)
		        {
		            arr.add(i);
		            n = n/i;
		        }
		    }
		    // This condition is to handle the case when n is a prime number
		    // greater than 2
		    if (n > 2)
		        arr.add(n);
		    
		    return arr;
		}
	
		public static int expo(int a, int b){
			if (b==0)
		        return 1;
		    if (b==1)
		        return a;
		    if (b==2)
		        return a*a;
	
		    if (b%2==0){
		            return expo(expo(a,b/2),2);
		    }
		    else{
		        return a*expo(expo(a,(b-1)/2),2);
		    }
		}
		static class Pair implements Comparable<Pair>
		{
			int f;
			int s;
			Pair(int ii, int cc)
			{
				f=ii;
				s=cc;
			}
			
			public int compareTo(Pair o) 
			{
				return Integer.compare(this.f, o.f);
			}
			
		}
		
		public static int[] sieve(int N){    // O(n*log(logn))
			int arr[]= new int[N+1];
			for(int i=2;i<=Math.sqrt(N);i++){
				if(arr[i]==0){
					for(int j= i*i;j<= N;j= j+i){
						arr[j]=1;
					}
				}
			}
			return arr;
			// All the i for which arr[i]==0 are prime numbers.
		}
		static long gcd(long a,long b){       // O(logn)
			if(b==0) return a;
			return gcd(b,a%b);
		}
		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());
		    }
		  }
	}