Problem: After waking up at hh:mm, Andrew realised that he had forgotten to feed his only cat for yet another time (guess why there's only one cat). The cat's current hunger level is H points, moreover each minute without food increases his hunger by D points.

At any time Andrew can visit the store where tasty buns are sold (you can assume that is doesn't take time to get to the store and back). One such bun costs C roubles and decreases hunger by N points. Since the demand for bakery drops heavily in the evening, there is a special 20% discount for buns starting from 20:00 (note that the cost might become rational). Of course, buns cannot be sold by parts.

Determine the minimum amount of money Andrew has to spend in order to feed his cat. The cat is considered fed if its hunger level is less than or equal to zero.

Input

The first line contains two integers hh and mm (00 ≤ hh ≤ 23, 00 ≤ mm ≤ 59) — the time of Andrew's awakening.

The second line contains four integers H, D, C and N (1 ≤ H ≤ 105, 1 ≤ D, C, N ≤ 102).

Output

Output the minimum amount of money to within three decimal digits. You answer is considered correct, if its absolute or relative error does not exceed 10 - 4.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

19 00
255 1 100 1


Output

25200.0000


Input

17 41
1000 6 15 11


Output

1365.0000

Note

In the first sample Andrew can visit the store at exactly 20:00. The cat's hunger will be equal to 315, hence it will be necessary to purchase 315 buns. The discount makes the final answer 25200 roubles.

In the second sample it's optimal to visit the store right after he wakes up. Then he'll have to buy 91 bins per 15 roubles each and spend a total of 1365 roubles.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class cf1 {
	InputStream is;
	PrintWriter out;
	int dx[]= {0,0,1,-1,+1,-1,+1,-1},dy[]={+1,-1,0,0,1,-1,-1,1};
	static long mod=pow(10,9)+7;
	
	void solve() throws Exception 
	{
		int hh=ni();
		int mm=ni();
		int h=ni();
		int d=ni();
		int c=ni();
		int n=ni();
		int min=hh*60+mm;
		int dis=20*60;
		int cost=(h/n)*c;
		if(h%n!=0)
			cost+=c;
		double ccco=(double)cost;
		if(min>=20*60)
			ccco*=0.8;
		if(dis>=min)
			h+=(dis-min)*d;
		else
			h+=((60*24)-(min-dis))*d;
		double cc=((double)c)*0.8;
		int item=h/n;
		if(h%n!=0)
			item++;
		double cco=((double)item)*cc;
		if(ccco<cco)
			out.println(ccco);
		else
			out.println(cco);
		out.flush();
	}
	
	int small[];
	void pre(int n) 
	{
		small=new int[n+1];
		for(int i=2;i*i<=n;i++) 
		{
			for(int j=i;j*i<=n;j++)
			{
				if(small[i*j]==0)
					small[i*j]=i;
			}
		}
		for(int i=0;i<=n;i++)
		{
			if(small[i]==0)
				small[i]=i;
		}
	}
	static long d, x, y;
	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;
	    }
	}
	long modInverse(long A,long M) //A and M are coprime 
	{
	    extendedEuclid(A,M);
	    return (x%M+M)%M;    //x may be negative
	}
	public static void mergeSort(int[] arr, int l ,int r) 
	{
		if((r-l)>=1) 
		{
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(int arr[], int l, int r, int mid) 
	{
		int n1 = (mid-l+1), n2 = (r-mid);
		int left[] = new int[n1];
		int right[] = new int[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2) 
		{
			if(left[i]>right[j]) 
			{
				arr[k++] = right[j++];
			}
			else 
			{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	public static void mergeSort(long[] arr, int l ,int r) 
	{
		if((r-l)>=1) 
		{
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(long arr[], int l, int r, int mid) 
	{
		int n1 = (mid-l+1), n2 = (r-mid);
		long left[] = new long[n1];
		long right[] = new long[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2)
		{
			if(left[i]>right[j]) 
			{
				arr[k++] = right[j++];
			}
			else
			{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	 static class Pair implements Comparable<Pair> 
	 {
		 
	       long x,y,k;
	       int i,dir;
	       long cost;
		Pair (long x,long y) 
		{ 
			this.x=x;
			this.y=y;
		}   
		public int compareTo(Pair o) 
		{
			return Long.compare(this.y,o.y);
		}
	 
		public String toString() 
		{
			return x+" "+y+" "+k+" "+i;}
		public boolean equals(Object o) 
		{
			if (o instanceof Pair) 
			{
				Pair p = (Pair)o;
				return p.x == x && p.y == y;
			}
			return false;
		}
		public int hashCode() 
		{
			return new Long(y).hashCode()*31 + new Long(x).hashCode() ;
		}
	} 
	    public static boolean isPal(String s) 
	    {
	        for(int i=0, j=s.length()-1;i<=j;i++,j--) 
	        {
	                if(s.charAt(i)!=s.charAt(j)) return false;
	        }
	        return true;
	    }
	    public static String rev(String s) 
	    {
			StringBuilder sb=new StringBuilder(s);
			sb.reverse();
			return sb.toString();
	    }
	    
	    public static long gcd(long x,long y) 
	    {
		if(x%y==0)
			return y;
		else
			return gcd(y,x%y);
	    }
	    
	    public static int gcd(int x,int y) 
	    {
		if(y==0)
			return x;
		else 
			return gcd(y,x%y);
	    }
	    
	    public static long gcdExtended(long a,long b,long[] x) 
	    {    
	        if(a==0) 
	        {
	            x[0]=0;
	            x[1]=1;
	            return b;
	        }
	        long[] y=new long[2];
	        long gcd=gcdExtended(b%a, a, y);
	        
	        x[0]=y[1]-(b/a)*y[0];
	        x[1]=y[0];
	        
	        return gcd;
	    }
	    
	    public static int abs(int a,int b) 
	    {
		return (int)Math.abs(a-b);
	    }
	 
	    public static long abs(long a,long b) 
	    {
		return (long)Math.abs(a-b);
	    }
	    
	    public static int max(int a,int b) 
	    {
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static int min(int a,int b) 
	    {
		if(a>b)
			return b;
		else 
			return a;
	    }
	    
	    public static long max(long a,long b) 
	    {
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static long min(long a,long b) 
	    {
		if(a>b)
			return b;
		else 
			return a;
	    }
	 
	    public static long pow(long n,long p,long m) 
	    {
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	    }
	    
	    public static long pow(long n,long p) 
	    {
		long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0) 
		{
		    if(p%2==1)
		        result *= n;	    
		    p >>=1;
		    n*=n;	    
		}
		return result;
	    }
	    public static void debug(Object... o) 
	    {
			System.out.println(Arrays.deepToString(o));
		}
	    void run() throws Exception 
	    {
			is = System.in;
			out = new PrintWriter(System.out);
			solve();
			out.flush();
		}
	   
	    public static void main(String[] args) throws Exception 
	    {
			new Thread(null, new Runnable() 
			{
				public void run() 
				{
					try 
					{
						new cf1().run();
					} catch (Exception e) 
					{
						e.printStackTrace();
					}
				}
			}, "1", 1 << 26).start();
		}
	    private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte()
		{
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) 
			{
				ptrbuf = 0;
				try 
				{
					lenbuf = is.read(inbuf);
				} catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) 
		{
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() 
		{
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b));
			return b;
		}
	 
		private double nd() 
		{
			return Double.parseDouble(ns());
		}
	 
		private char nc() 
		{
			return (char) skip();
		}
	 
		private String ns() 
		{
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) 
			{ // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) 
		{
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) 
			{
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) 
		{
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) 
		{
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() 
		{
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') 
			{
				minus = true;
				b = readByte();
			}
	 
			while (true)
			{
				if (b >= '0' && b <= '9') 
				{
					num = num * 10 + (b - '0');
				} else 
				{
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() 
		{
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') 
			{
				minus = true;
				b = readByte();
			}
	 
			while (true)
			{
				if (b >= '0' && b <= '9') 
				{
					num = num * 10 + (b - '0');
				} else 
				{
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
}