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.io.*;
     
     
     
     
    import java.math.*;
    import java.util.*;
import java.util.concurrent.DelayQueue;    
          public class Problem
           {
            private InputStream is;
            private PrintWriter out;
            static int MOD = (int)(1e9+7);
            ArrayList<Integer>[] amp;
            public static void main(String[] args) throws Exception
            {
                new Thread(null, new Runnable()
                {
                public void run()
                {
                    try {
         } catch (Exception e)
                    {
                        System.out.println(e);
                    }
                }
            }, "1", 1 << 26).start();
                new Problem().soln();
            }
            char ch[][];
            static ArrayList<Integer>[] g=new ArrayList[100001];
            static ArrayList<Integer> ar[];
            static long ok[];    
            static int phi[]=new int[500005];
            static int dp[][];
            void solve()
            {
            int hh=ni();
            int mm=ni();
            double h=ni();
            double d=ni();
            double c=ni();
            double n=ni();
            
            if(hh<20){
				double fin = (int)Math.ceil(h/n);
				double pc = 0.8*c;
				double ss = 60*(20-hh);
				ss-=mm;
				double finq1 = (int) Math.ceil((h + ss* d)/ n);

				System.out.printf("%.4f",Math.min(fin * c,finq1 * pc));
				
			return;
			}
            double fin = (int)Math.ceil(h/n);
			double price = 0.8*c;
			System.out.printf("%.4f",fin * price);
			
            

            }
             
            public static long query(int v,int start,int end,int l,int r,int x)
            {
            	if(r < start || end < l)
                {
                    return 0;
                }
                if(l <= start && end <= r)
                {
                    return (tre[v]);
                }
                int mid = (start + end) / 2;
                long p1 = query(2*v, start, mid, l, r,x);
                long p2 = query(2*v+1, mid+1, end, l, r,x);
                return p1+p2;	
            }
            public static void update(int v,int tl,int tr,long l,long harami2)
            {
            	if(tl==tr)
                {
                    tre[v]=harami2;
                }
                else
                {
                    int mid=(tl+tr)/2;
                    if(tl <= l &&l <= mid)
                    {
                        update(2*v,tl, mid, l, harami2);
                    }
                    else
                    {
                        update(2*v+1,mid+1,tr, l, harami2);
                    }
                    tre[v]=tre[2*v]+tre[2*v+1];
                }
            }
            static long tre[]=new long[8000005];
            static ArrayList<String> dictionary = new ArrayList();
            public static void wordBreakUtil(String s,int n,String result)
            {
            	for(int i=1;i<=n;i++)
            	{
            		String prefix = s.substring(0,i);
            		if(dictionary.contains(prefix))
            		{
            			if(i==n)
            			{
            				result+=prefix;
            				System.out.println(result);
            				return;
            			}
            			wordBreakUtil(s.substring(i),n-i,result+prefix+" ");
            		}
            	}
            }
            public static void permute(char s[],int l,int r)
            {
            	if(l==r)
            	{
            		System.out.println(new String(s));
            	}
            	else
            	{
            		for(int i=l;i<=r;i++)
            		{
            			char temp=s[i];
            			s[i]=s[l];
            			s[l]=temp;
            			permute(s,l+1,r);
            			temp=s[i];
            			s[i]=s[l];
            			s[l]=temp;
            		}
            	}
            }
            public static void StockSpan(int a[],int n)
            {
            	Stack<Integer> st = new Stack();
            	st.push(0);
            	int S[]=new int[n];
            	S[0]=1;
            	for(int i=1;i<n;i++)
            	{
            		while(!st.isEmpty()&&a[st.peek()]<=a[i])
            			st.pop();
            		S[i]=(st.isEmpty())?(i+1):(i-st.peek());
            		st.push(i);
            	}
            	for(int i=0;i<n;i++)
            		System.out.print(S[i]+" ");
            }
            
            
            public static void MaxSum(int a[][],int r,int c)
            {
            	int ans=0;
            	for(int i=0;i<r/2;i++)
            	{
            		for(int j=0;j<c/2;j++)
            		{
            			int r1=i;
            			int c1=j;
            			int r2=r-i-1;
            			int c2=c-j-1;
            			ans+=Math.max(Math.max(a[r1][c1],a[r1][c2]),Math.max(a[r2][c1],a[r2][c2]));
            		}
            	}
            	System.out.println(ans);
            
            }
            
            
            public static void Dia(int a[][],int row,int col)
            {
            	for(int line=1;line<=(row+col-1);line++)
            	{
            		int start_col = Math.max(0,line-row);
            		int count = Math.min(line,Math.min(row,col-start_col));
            		for(int j=0;j<count;j++)
            		{
            			System.out.print(a[Math.min(row,line)-j-1][start_col+j]+" ");
            		}
            		System.out.println();
            	}
            }

			public static void AntiClock(int a[][],int n)
            
            {
            	for(int i=0;i<n;i++)
            	{
            		for(int j=i;j<n;j++)
            		{
            			int tmp=a[i][j];
            			a[i][j]=a[j][i];
            			a[j][i]=tmp;
            		}
            	}
            	for(int i=0;i<n/2;i++)
            	{
            		for(int j=0;j<n;j++)
            		{
            			int tmp=a[i][j];
            			a[i][j]=a[n-1-i][j];
            			a[n-1-i][j]=tmp;
            		}
            	}
            	
            }
            
           
            
            
            
            
            public static long pr(long x,long y,long m)
            {
            	if(y==0)
            		return 1;
            	long p = pr(x,y/2,m);
            	p=(p*p)%m;
            	return(y%2==0)?(p):(x*p%m);
            }
            public static long GCD(long x,long y)
            {
            	if(y==0)
            		return x;
            	else
            		return GCD(y,x%y);
            }
            
            public static void print(ArrayList<Integer> ar)
            {
            	Collections.sort(ar,Collections.reverseOrder());
            	System.out.println("Yes");
            	for(int x:ar)
            	{
            		System.out.print(x+" ");
            	}
            	return;
            }
            public static void LOL()
            {
            	/*int a[]=new int[5];
            	a[0]=2;a[1]=1;a[2]=4;a[3]=3;a[4]=5;
            	 System.out.println(LIS(a,5));
            	 int n=5;
            	 int dp[]=new int[n];
            	 for(int i=0;i<n;i++)
            		 dp[i]=1;
            	 
            	 int backtrack[]=new int[n];
            	 Arrays.fill(backtrack,-1);
            	 for(int i=1;i<n;i++)
            	 {
            		 for(int j=0;j<i;j++)
            		 {
            			 if(dp[j]+1>dp[i]&&a[j]<a[i])
            			 {
            				 dp[i]=dp[j]+1;
            				 backtrack[i]=j;
            			 }
            		 }
            	 }
            	 int index=-1;
            	 int max=0;
            	 for(int i=0;i<n;i++)
            	 {
            		 if(max<dp[i])
            		 {
            			 index=i;
            			 max=dp[i];
            		 }
            	 }
            	 
            	 int tmp=index;
            	 Stack<Integer> st=new Stack();
            	 while(tmp>=0)
            	 {
            		 st.push(a[tmp]);
            		 tmp=backtrack[tmp];
            	 }
            	 while(!st.isEmpty())
            	 {
            		 out.print(st.pop()+" ");
            	 }
            /*	int n=150;
            	int ugly[]=new int[n+1];
            	ugly[0]=1;
            	int next_multiple_of_2=2;
            	int next_multiple_of_3=3;
            	int next_multiple_of_5=5;
            	int i2=0;int i3=0;int i5=0;
            	for(int i=1;i<n;i++)
            	{
            		int min=Math.min(next_multiple_of_5, Math.min(next_multiple_of_3, next_multiple_of_2));
            		ugly[i]=min;
            		if(min==next_multiple_of_2)
            		{
            			i2++;
            			next_multiple_of_2=ugly[i2]*2;
            		}
            		if(min==next_multiple_of_3)
            		{
            			i3++;
            			next_multiple_of_3=ugly[i3]*3;
            		}
            		if(min==next_multiple_of_5)
            		{
            			i5++;
            			next_multiple_of_5=ugly[i5]*5;
            		}
            	}
            	System.out.println(ugly[n-1]);
            	
            	int t=ni();
            	while(t-->0)
            	{
            		long n=nl();
            		int a[]=new int[4];
            		a[0]=2;
            		a[1]=3;
            		a[2]=5;
            		a[3]=7;
            		long sucks=0;
            		for(int i=0;i<(1<<4);i++)
            		{
            			int count=0;
            			long curr=1;
            			for(int j=0;j<4;j++)
            			{
            				int x=i;
            				x&=(1<<j);
            				if(x>0)
            				{
            					curr*=(long)a[j];
            					count++;
            				}
            			}
            			if(count==0)
            				continue;
            			if(count%2==1)
            			{
            				sucks+=(n/curr);
            			}
            			else
            			{
            				sucks-=(n/curr);
            			}
            		}
            		out.println(n-sucks);
            	}
            	String s1=ns();
            	String s2=ns();
            	int m=s1.length();int n=s2.length();
            	int dp[][]=new int[m+1][n+1];
            	for(int i=0;i<=m;i++)
            	{
            		for(int j=0;j<=n;j++)
            		{
            			if(i==0)
            				dp[i][j]=j;
            			else if(j==0)
            				dp[i][j]=i;
            			else if(s1.charAt(i-1)==s2.charAt(j-1))
            				dp[i][j]=dp[i-1][j-1];
            			else
            				dp[i][j]=1+Math.min(dp[i-1][j-1],Math.min(dp[i-1][j],dp[i][j-1]));
            		}
            	}*/
            }
            public static int edit(String s1,String s2,int m,int n)
            {
            	if(m==0)
            		return n;
            	if(n==0)
            		return m;
            	if(s1.charAt(m-1)==s2.charAt(n-1))
            		return edit(s1,s2,m-1,n-1);
            	return 1+Math.min(edit(s1,s2,m,n-1),Math.min(edit(s1,s2,m-1,n),edit(s1,s2,m-1,n-1)));
            }
            static int max=1;
            public static int LIS(int a[],int n  )
            {
            	if(n==1)
            		return 1;
            	int res=1;
            	int max_ending_here=1;
            	for(int i=1;i<n;i++)
            	{
            		res=LIS(a,i);
            		if(a[i-1]<a[n-1]&&res+1>max_ending_here)
            			max_ending_here=res+1;
            	}
            	max=Math.max(max,max_ending_here);
            	return max_ending_here;
            }
            static boolean visi1[];
            static int cont=0;
            static int para[];
            public static void dfs(int curr,int pr)
            {
            	visi1[curr]=true;
            	
            	int trees=0;
            	for(int x:g[curr])
            	{
            		if(!visi1[x]&&x!=pr)
            		{
            			trees++;
            			dfs(x,pr);
            		}
            	}
            	if(trees==0)cont++;
            }
            
            static boolean visited[][];
			static int a[][];
            
          /* public static int find(int v,int start,int end,int l,int r)
            {
                if(r < start || end < l)
                {
                    return Integer.MIN_VALUE;
                }
                if(l <= start && end <= r)
                {
                    return (tre[v]);
                }
                int mid = (start + end) / 2;
                int p1 = find(2*v, start, mid, l, r);
                int p2 = find(2*v+1, mid+1, end, l, r);
                return Math.max(p1, p2);          
            }
            static int tre[]=new int[4000005];
            public static void Update(int v,int tl,int tr,int index,int val)
            {
                if(tl==tr)
                {
                    tre[v]=val;
                }
                else
                {
                    int mid=(tl+tr)/2;
                    if(tl <= index &&index <= mid)
                    {
                        Update(2*v,tl, mid, index, val);
                    }
                    else
                    {
                        Update(2*v+1,mid+1,tr, index, val);
                    }
                    tre[v]=(Math.max(tre[2*v],tre[2*v+1]));
                }
            }
            */
            
            static int d,x,y;
            static void exE(int a,int b)
            {
            	if(b==0)
            	{
            		d=a;
            		x=1;
            		y=0;
            	}
            	else
            	{
            		exE(b,a%b);
            		int tmp=x;
            		x=y;
            		y=tmp - (a/b)*y;
            	}
            }
            boolean isPrime(int x)
                {
                if(x==0||x==1)
                    return false;
                for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
                return true;
            }
            int  p ;
            long modInverse(long a, long mOD2){
                return  power(a, mOD2-2, mOD2);
            }
            long power(long x, long y, long m)
            {
            if (y == 0)
            return 1;
            long p = power(x, y/2, m) % m;
            p = (p * p) % m;
        
            return (y%2 == 0)? p : (x * p) % m;
            }
            public static long gcd(long a, long b){
                if(b==0) return a;
                return gcd(b,a%b);
            }
            class Pair1 implements Comparable<Pair1>{
                long a;
               
                double c;
                long b;
                Pair1(long x,double z,long y){
                this.a=x;
                              this.c=z;
                              this.b=y;
                }
                public int hashCode() {
                    return Objects.hash();
                }
                
                @Override
                public int compareTo(Pair1 arg0) {
                    if(c!=arg0.c)
                	return (int)(c-arg0.c);
                    else
                    	return (int)(arg0.b-b);
                }    
            }
            long power(long x, long y, int mod){
                long ans = 1;
                while(y>0){
                    if(y%2==0){
                        x = (x*x)%mod;
                        y/=2;
                    }
                    else{
                        ans = (x*ans)%mod;
                        y--;
                    }
                }
                return ans;
            }
            void soln() {
                is = System.in;
                out = new PrintWriter(System.out);
                long s = System.currentTimeMillis();
                solve();
                out.flush();
            }
             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))) {
                    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 int[][] nm(int n, int m) {
                int[][] map = new int[n][m];
                for (int i = 0; i < n; i++)
                {
                    for(int j=0;j<m;j++)
                        map[i][j]=ni();
                }
                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();
                }
            }
            private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
            private void tr(Object... o) {
                if (!oj)
                    System.out.println(Arrays.deepToString(o));
            }
        }