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:
//package CodeForces;

/*In the name of Allah the Most Merciful.
 * Author
 * Md. Toufiqul Islam
 * Dept. Of CSE
 * Ahsanullah University Of Science And Technology
*/
import java.io.*;
import java.math.*;
import java.util.*;
public class R471A {
    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
        OutputWriter out  = new OutputWriter(System.out);

        int hh = sc.nextInt();
        int mm = sc.nextInt();

        int h = sc.nextInt();
        int d = sc.nextInt();

        int c = sc.nextInt();
        int n = sc.nextInt();

        double total = 0;



        if(hh>=20 && hh<=23){

            double temp = Math.ceil(h/(double)n);


            double price = c-(0.2*c);

            total += temp*price;

        }
        else{
            double temp = Math.ceil(h/(double)n);



            double total1 = temp*c;

            int time1 = hh*60+mm;
            int time2 = 20*60+0;

            int timeDif = (time2-time1);
            int totalhunger = timeDif *d+h;

            double temp1 = Math.ceil(totalhunger/(double)n);


            double price = c-(0.2*c);

            double total2 = temp1*price;



            total = Math.min(total1,total2);


        }

        out.printf("%.4f",total);

        out.close();
    }

     public static class InputReader {
             private boolean finished = false;

             private InputStream stream;
             private byte[] buf = new byte[1024];
             private int curChar;
             private int numChars;
             private SpaceCharFilter filter;

             public InputReader(InputStream stream) {
                 this.stream = stream;
             }

             public 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++];
             }

             public int peek() {
                 if (numChars == -1) {
                     return -1;
                 }
                 if (curChar >= numChars) {
                     curChar = 0;
                     try {
                         numChars = stream.read(buf);
                     } catch (IOException e) {
                         return -1;
                     }
                     if (numChars <= 0) {
                         return -1;
                     }
                 }
                 return buf[curChar];
             }

             public 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;
             }

             public 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;
             }

             public String nextString() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 StringBuilder res = new StringBuilder();
                 do {
                     if (Character.isValidCodePoint(c)) {
                         res.appendCodePoint(c);
                     }
                     c = read();
                 } while (!isSpaceChar(c));
                 return res.toString();
             }

             public boolean isSpaceChar(int c) {
                 if (filter != null) {
                     return filter.isSpaceChar(c);
                 }
                 return isWhitespace(c);
             }

             public static boolean isWhitespace(int c) {
                 return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
             }

             private String readLine0() {
                 StringBuilder buf = new StringBuilder();
                 int c = read();
                 while (c != '\n' && c != -1) {
                     if (c != '\r') {
                         buf.appendCodePoint(c);
                     }
                     c = read();
                 }
                 return buf.toString();
             }

             public String readLine() {
                 String s = readLine0();
                 while (s.trim().length() == 0) {
                     s = readLine0();
                 }
                 return s;
             }

             public String readLine(boolean ignoreEmptyLines) {
                 if (ignoreEmptyLines) {
                     return readLine();
                 } else {
                     return readLine0();
                 }
             }

             public BigInteger readBigInteger() {
                 try {
                     return new BigInteger(nextString());
                 } catch (NumberFormatException e) {
                     throw new InputMismatchException();
                 }
             }

             public char nextCharacter() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 return (char) c;
             }

             public double nextDouble() {
                 int c = read();
                 while (isSpaceChar(c)) {
                     c = read();
                 }
                 int sgn = 1;
                 if (c == '-') {
                     sgn = -1;
                     c = read();
                 }
                 double res = 0;
                 while (!isSpaceChar(c) && c != '.') {
                     if (c == 'e' || c == 'E') {
                         return res * Math.pow(10, nextInt());
                     }
                     if (c < '0' || c > '9') {
                         throw new InputMismatchException();
                     }
                     res *= 10;
                     res += c - '0';
                     c = read();
                 }
                 if (c == '.') {
                     c = read();
                     double m = 1;
                     while (!isSpaceChar(c)) {
                         if (c == 'e' || c == 'E') {
                             return res * Math.pow(10, nextInt());
                         }
                         if (c < '0' || c > '9') {
                             throw new InputMismatchException();
                         }
                         m /= 10;
                         res += (c - '0') * m;
                         c = read();
                     }
                 }
                 return res * sgn;
             }

             public boolean isExhausted() {
                 int value;
                 while (isSpaceChar(value = peek()) && value != -1) {
                     read();
                 }
                 return value == -1;
             }

             public String next() {
                 return nextString();
             }

             public SpaceCharFilter getFilter() {
                 return filter;
             }

             public void setFilter(SpaceCharFilter filter) {
                 this.filter = filter;
             }

             public interface SpaceCharFilter {
                 public boolean isSpaceChar(int ch);
             }
             public int[] nextIntArray(int n){
                 int[] array=new int[n];
                 for(int i=0;i<n;++i)array[i]=nextInt();
                 return array;
             }
             public int[] nextSortedIntArray(int n){
                 int array[]=nextIntArray(n);
                 Arrays.sort(array);
                 return array;
             }
             public int[] nextSumIntArray(int n){
                 int[] array=new int[n];
                 array[0]=nextInt();
                 for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
                 return array;
             }
             public long[] nextLongArray(int n){
                 long[] array=new long[n];
                 for(int i=0;i<n;++i)array[i]=nextLong();
                 return array;
             }
             public long[] nextSumLongArray(int n){
                 long[] array=new long[n];
                 array[0]=nextInt();
                 for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
                 return array;
             }
             public long[] nextSortedLongArray(int n){
                 long array[]=nextLongArray(n);
                 Arrays.sort(array);
                 return array;
             }
         }
      public static class OutputWriter {
              private final PrintWriter writer;

              public OutputWriter(OutputStream outputStream) {
                  writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
              }

              public OutputWriter(Writer writer) {
                  this.writer = new PrintWriter(writer);
              }

              public void print(char[] array) {
                  writer.print(array);
              }

              public void print(Object... objects) {
                  for (int i = 0; i < objects.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(objects[i]);
                  }
              }

              public void print(int[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void print(double[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void print(long[] array) {
                  for (int i = 0; i < array.length; i++) {
                      if (i != 0) {
                          writer.print(' ');
                      }
                      writer.print(array[i]);
                  }
              }

              public void println(int[] array) {
                  print(array);
                  writer.println();
              }

              public void println(double[] array) {
                  print(array);
                  writer.println();
              }

              public void println(long[] array) {
                  print(array);
                  writer.println();
              }

              public void println() {
                  writer.println();
              }

              public void println(Object... objects) {
                  print(objects);
                  writer.println();
              }

              public void print(char i) {
                  writer.print(i);
              }

              public void println(char i) {
                  writer.println(i);
              }

              public void println(char[] array) {
                  writer.println(array);
              }

              public void printf(String format, Object... objects) {
                  writer.printf(format, objects);
              }

              public void close() {
                  writer.close();
              }

              public void flush() {
                  writer.flush();
              }

              public void print(long i) {
                  writer.print(i);
              }

              public void println(long i) {
                  writer.println(i);
              }

              public void print(int i) {
                  writer.print(i);
              }

              public void println(int i) {
                  writer.println(i);
              }

              public void separateLines(int[] array) {
                  for (int i : array) {
                      println(i);
                  }
              }
          }

}