Problem: IT City administration has no rest because of the fame of the Pyramids in Egypt. There is a project of construction of pyramid complex near the city in the place called Emerald Walley. The distinction of the complex is that its pyramids will be not only quadrangular as in Egypt but also triangular and pentagonal. Of course the amount of the city budget funds for the construction depends on the pyramids' volume. Your task is to calculate the volume of the pilot project consisting of three pyramids — one triangular, one quadrangular and one pentagonal.

The first pyramid has equilateral triangle as its base, and all 6 edges of the pyramid have equal length. The second pyramid has a square as its base and all 8 edges of the pyramid have equal length. The third pyramid has a regular pentagon as its base and all 10 edges of the pyramid have equal length.

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Input

The only line of the input contains three integers l3, l4, l5 (1 ≤ l3, l4, l5 ≤ 1000) — the edge lengths of triangular, quadrangular and pentagonal pyramids correspondingly.

Output

Output one number — the total volume of the pyramids. Absolute or relative error should not be greater than 10 - 9.

Examples

Input

2 5 3


Output

38.546168065709

Solution (in JAVA):

Solution:
/*
 * The MIT License
 *
 * Copyright 2016 Mouad NACIRI <mouadnaciri1@gmail.com>.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 *
 * @author NACIRI Mouad <mouadnaciri1@gmail.com>
 * @version 1.5.1
 */

public class MainA {
    /* VIP, DON'T TOUCH!! */
    static StringTokenizer ST;
    static BufferedReader IN;
    static BufferedWriter OUT;
    static {
        IN = new BufferedReader(new InputStreamReader(System.in));
        OUT = new BufferedWriter(new OutputStreamWriter(System.out));
    }
    
    public static void main(String[] args) throws IOException {
        ll();
        /*long x = nl();
        
        long nf = x * (x-1) * (x-2) * (x-3) * (x-4);
        
        long out = (nf * (x-5)*(x-6)) / 5040 + (nf * (x-5)) / 720 + nf/120; */
        
        long l1 = nl(), l2 = nl(), l3 = nl();


        double a = Math.pow(l1,3)/(6*Math.sqrt(2)),
                b = Math.pow(l2,3)*Math.sqrt(2)/6,
                c = Math.pow(l3,3)*((5+Math.sqrt(5))/24);
        double out = a+b+c;

        System.out.printf("%.12f \n",out);
        
        cAll();
    }
    
    //IO stuff...
    static void ll() throws IOException { ST = new StringTokenizer(nlnt()); }
    static void ll(String del) throws IOException { ST = new StringTokenizer(nlnt(), del); }
    static void ll(String s, String del) throws IOException { ST = new StringTokenizer(s, del); }
    static void ll(String s, char c) throws IOException { ST = new StringTokenizer(s); }
    
    static int tlen() { return ST.countTokens(); }
    static boolean hn() { return ST.hasMoreTokens(); }
    static String n() throws IOException { return ST.nextToken(); }
    static String nln() throws IOException {
        String l;
        while((l = IN.readLine()) != null && l.trim().length() == 0) {}
        return l;
    }
    static String nlnt() throws IOException {
        String l;
        while((l = IN.readLine()) != null && (l = l.trim()).length() == 0) {}
        return l;
    }
    static boolean nbl() throws IOException { return Boolean.parseBoolean(ST.nextToken()); }
    static byte nb() throws IOException { return Byte.parseByte(ST.nextToken()); }
    static byte nb(int radix) throws IOException { return Byte.parseByte(ST.nextToken(), radix); }
    static double nd() throws IOException { return Double.parseDouble(ST.nextToken()); }
    static float nf() throws IOException { return Float.parseFloat(ST.nextToken()); }
    static int ni() throws IOException { return Integer.parseInt(ST.nextToken()); }
    static int ni(int radix) throws IOException { return Integer.parseInt(ST.nextToken(), radix); }
    static long nl() throws IOException { return Long.parseLong(ST.nextToken()); }
    static long nl(int radix) throws IOException { return Long.parseLong(ST.nextToken(), radix); }
    static short ns() throws IOException { return Short.parseShort(ST.nextToken()); }
    static short ns(int radix) throws IOException { return Short.parseShort(ST.nextToken(), radix); }
    
    static void p(String s) throws IOException { OUT.write(s); }
    static void p(char c) throws IOException { OUT.write(c); }
    static void p(char s[]) throws IOException { OUT.write(s); }
    static void pl(String s) throws IOException { OUT.write(s); OUT.newLine(); }
    static void pl(char c) throws IOException { OUT.write(c); OUT.newLine(); }
    static void pl(char s[]) throws IOException { OUT.write(s); OUT.newLine(); }
    static void pl() throws IOException { OUT.newLine(); }
    static void cAll() throws IOException { IN.close(); OUT.close(); }
    
}