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.io.*;
		import java.math.BigInteger;
		import java.util.*;
			
			
			public class Practice {
				private static InputStream stream;
				private static byte[] buf = new byte[1024];
				private static int curChar;
				private static int numChars;
				private static SpaceCharFilter filter;
				private static PrintWriter pw;
				private static long mod=1000000007;
			
			    public static void main(String[] args) {
			    	InputReader(System.in);
					pw = new PrintWriter(System.out); 
			        new Thread(null ,new Runnable(){
			           public void run(){
			               try{
			                   solve();//This is solution method
		               pw.close();
		           } catch(Exception e){
		               e.printStackTrace();
		           }
		       }
		   },"1",1<<26).start();
			    				   }
			    public static void Merge(long a[],int p,int r){
		            if(p<r){
		                int q = (p+r)/2;
		                Merge(a,p,q);
		                Merge(a,q+1,r);
		                Merge_Array(a,p,q,r);
		            }
		        }
		        public static void Merge_Array(long a[],int p,int q,int r){
		           long b[] = new long[q-p+1];
		            long c[] = new long[r-q];
		            for(int i=0;i<b.length;i++)
		                b[i] = a[p+i];
		            for(int i=0;i<c.length;i++)
		                c[i] = a[q+i+1];
		            int i = 0,j = 0;
		            for(int k=p;k<=r;k++){
		                if(i==b.length){
		                    a[k] = c[j];
		                    j++;
		                }
		                else if(j==c.length){
		                    a[k] = b[i];
		                    i++;
		                }
		                else if(b[i]<c[j]){
		                    a[k] = b[i];
		                    i++;
		                }
		                else{
		                    a[k] = c[j];
		                    j++;
		                }
		            }
		        }    
			    				    
	    					public static void solve() {
	        		    	
	    						String s=nextLine();
	    						long dp[]=new long[s.length()];
	    						if((s.charAt(0)-'0')%4==0){
	    							dp[0]++;
	    						}
	    						for(int i=1;i<s.length();i++){
	    							dp[i]=dp[i-1];
	    							int last_two= (s.charAt(i)-'0')+(s.charAt(i-1)-'0')*10;
	    							if(last_two%4==0){
	    								dp[i]+=i;
	    							}
	    							if((s.charAt(i)-'0')%4==0){
		    							dp[i]++;
		    						}
	    						}
	    						pw.println(dp[s.length()-1]);
	        		    
	        		    	}
	        		    	
	        		        
	        		    	 	
		        		    		
		        		    				
		        		        
		public static boolean isVowel(char c){        		    		
			if(c=='a' || c=='i'|| c=='e' || c=='o' || c=='u')
					return true;
				return false;
			}
			
			
		    public static String reverseString(String s) {
				StringBuilder sb = new StringBuilder(s);
				sb.reverse();
				return (sb.toString());
			}
		    private static BigInteger ncr(int n,int k){
		    	if (k < 0 || k > n) return BigInteger.ZERO;
		        if (n-k < k) k = n-k;
		
		        BigInteger x = BigInteger.ONE;
		        for (int i = 1; i <= k; i++) {
		            x = x.multiply(new BigInteger(""+(n-i+1)));
		x = x.divide(new BigInteger(""+i));
		        }
		
		return x;
		    }
		    static long fact[];
		private static void factmod(int n,int mod){
			fact=new long[n+1];
			fact[0]=1;
			for(int i=1;i<=n;i++){
				fact[i]=i*fact[i-1];
				//fact[i]%=mod;
		
			}
			
		}
		private static long phi(long n){
			long ans=n;
			if(n%2==0)
				ans-=(ans/2);
			while(n%2==0)
			{
				n/=2;
				
			}
			for(int i=3;i*i<=n;i+=2){
				if(n%i==0){
				while(n%i==0){
					n/=i;
				}
				ans-=(ans/i);
				}
			}
			if(n>2)
				ans-=(ans/n);
			
			return ans;
		}
		static long d,x,y;
		static long modInverse(long A, long M)
		{
		extendedEuclid(A,M);
		return (x%M+M)%M;    //x may be negative
		}
		static void extendedEuclid(long A, long B) {
		if(B == 0) {
		d = A;
		x = 1;
		y = 0;
		}
		else {
		extendedEuclid(B, A%B);
		long temp = x;
		x = y;
		y = temp - (A/B)*y;
		}
		}
		static boolean prime[];
		static int spf[];
		public static void sieve(int n){
			prime=new boolean[n+1];
			spf=new int[n+1];
			
			Arrays.fill(spf, 1);
			Arrays.fill(prime, true);
		prime[1]=false;
			spf[2]=2;
			for(int i=4;i<=n;i+=2)
			{
				spf[i]=2;
				prime[i]=false;
			}
		
		for(int i=3;i<=n;i+=2){
			if(prime[i]){
				spf[i]=i;
				for(int j=2*i;j<=n;j+=i){
					
					prime[j]=false;
				if(spf[j]==1){
					spf[j]=i;
				}
				}
			}
		}
			
		}
		public static boolean isPrime(long n) {
			
			if (n <= 1)
				return false;
			if (n <= 3)
				return true;
		
			if (n % 2 == 0 || n % 3 == 0)
				return false;
		
			for (long i = 5; i * i <= n; i = i + 6)
				if (n % i == 0 || n % (i + 2) == 0)
					return false;
		
			return true;
		}
		
		    
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}
			
			
			public static void InputReader(InputStream stream1) {
				stream = stream1;
			}
		 
			private static boolean isWhitespace(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
		 
			private static boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		 
			private static int read() {
				if (numChars == -1)
					throw new InputMismatchException();
				if (curChar >= numChars) {
					curChar = 0;
					try {
						numChars = stream.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (numChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
		 
			private static int nextInt() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
			throw new InputMismatchException();
		res *= 10;
		res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		 
			private static long nextLong() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
			throw new InputMismatchException();
		res *= 10;
		res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		 
			private static String nextToken() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
		 
			private static String nextLine() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndOfLine(c));
				return res.toString();
			}
		 
			private static int[] nextIntArray(int n) {
				int[] arr = new int[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextInt();
				}
				return arr;
			}
		 
			private static int[][] next2dArray(int n, int m) {
				int[][] arr = new int[n][m];
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < m; j++) {
						arr[i][j] = nextInt();
					}
				}
				return arr;
			}
			private static char[][] nextCharArray(int n,int m){
				char [][]c=new char[n][m];
				for(int i=0;i<n;i++){
					String s=nextLine();
					for(int j=0;j<s.length();j++){
						c[i][j]=s.charAt(j);
					}
				}
				return c;
			}
		 
			private static long[] nextLongArray(int n) {
				long[] arr = new long[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextLong();
				}
				return arr;
			}
		 
			private static void pArray(int[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(long[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(boolean[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return isWhitespace(c);
			}
		 
			private interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		
			
		}	
			 class Hashing {
				 
				  static final int multiplier = 43;
				  static final Random rnd = new Random();
				  static final int mod1 = BigInteger.valueOf((int) (1e9 + rnd.nextInt((int) 1e9))).nextProbablePrime().intValue();
				  static final int mod2 = BigInteger.valueOf((int) (1e9 + rnd.nextInt((int) 1e9))).nextProbablePrime().intValue();
				  static final int invMultiplier1 = BigInteger.valueOf(multiplier).modInverse(BigInteger.valueOf(mod1)).intValue();
				  static final int invMultiplier2 = BigInteger.valueOf(multiplier).modInverse(BigInteger.valueOf(mod2)).intValue();
		 
				  long[] hash1, hash2;
				  long[] inv1, inv2;
				  int n;
		 
				  public Hashing(String s) {
				    n = s.length();
				    hash1 = new long[n + 1];
				    hash2 = new long[n + 1];
				    inv1 = new long[n + 1];
				    inv2 = new long[n + 1];
				    inv1[0] = 1;
				    inv2[0] = 1;
		 
				    long p1 = 1;
				    long p2 = 1;
				    for (int i = 0; i < n; i++) {
				      hash1[i + 1] = (hash1[i] + s.charAt(i) * p1) % mod1;
				      p1 = p1 * multiplier % mod1;
				      inv1[i + 1] = inv1[i] * invMultiplier1 % mod1;
				      hash2[i + 1] = (hash2[i] + s.charAt(i) * p2) % mod2;
				      p2 = p2 * multiplier % mod2;
				      inv2[i + 1] = inv2[i] * invMultiplier2 % mod2;
				    }
				  }
		 
				  public long getHash(int i, int r) {
					//  i--;
				    return (((hash1[r] - hash1[i] + mod1) * inv1[i] % mod1) << 32)
				        + (hash2[r] - hash2[i] + mod2) * inv2[i] % mod2;
				  }
			}