public static void enu2ecefCov(GMatrix ecefCov, GMatrix enuCov, LLA refLLA) {
    double lambda = refLLA.longitude;
    double phi = refLLA.latitude;
    
    GMatrix R = new GMatrix(6, 6);
    GMatrix Rt = new GMatrix(6, 6);
    GMatrix tmp1 = new GMatrix(6, 6);
    GMatrix tmp2 = new GMatrix(6, 6);
    
    R.setElement(0, 0, -Math.sin(lambda));
    R.setElement(0, 1, -Math.sin(phi)*Math.cos(lambda));
    R.setElement(0, 2, Math.cos(phi)*Math.cos(lambda));
    R.setElement(1, 0, Math.cos(lambda));
    R.setElement(1, 1, -Math.sin(phi)*Math.sin(lambda));
    R.setElement(1, 2, Math.cos(phi)*Math.sin(lambda));
    R.setElement(2, 0, 0);
    R.setElement(2, 1, Math.cos(phi));
    R.setElement(2, 2, Math.sin(phi));
    R.setElement(3, 3, -Math.sin(lambda));
    R.setElement(3, 4, -Math.sin(phi)*Math.cos(lambda));
    R.setElement(3, 5, Math.cos(phi)*Math.cos(lambda));
    R.setElement(4, 3, Math.cos(lambda));
    R.setElement(4, 4, -Math.sin(phi)*Math.sin(lambda));
    R.setElement(4, 5, Math.cos(phi)*Math.sin(lambda));
    R.setElement(5, 3, 0);
    R.setElement(5, 4, Math.cos(phi));
    R.setElement(5, 5, Math.sin(phi));

    Rt.transpose(R);
    tmp1.mul(enuCov, R);
    ecefCov.mul(Rt, tmp1);
}

public static String addBinary(){
 // The two input Strings, containing the binary representation of the two values:
    String input0 = "1010";
    String input1 = "10";

    // Use as radix 2 because it's binary    
    int number0 = Integer.parseInt(input0, 2);
    int number1 = Integer.parseInt(input1, 2);

    int sum = number0 + number1;
    return Integer.toBinaryString(sum); //returns the answer as a binary value;
}

import java.util.ArrayList;
import java.util.Iterator;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		char[] variables = setVariables(in);
		int[] minTerms = setMinTerms(in);
		String[] binaryMinTerms = decimalToBinary(variables, minTerms);
		
		ArrayList<Group> groups = computeSuccessiveGroups(minTerms, binaryMinTerms);
		
		displayInput(variables, minTerms);
		printPIs(groups, variables);
	}
	
	private static char[] setVariables(Scanner in) {
		System.out.print("Enter the number of variables: ");
		int numVariables = in.nextInt();
		char[] variables = new char[numVariables];
		
		System.out.print("Enter each variable separated by spaces: ");
		for(int i = 0; i < numVariables; i++) {
			variables[i] = in.next().charAt(0);
		}
		return variables;
	}
	
	private static int[] setMinTerms(Scanner in) {
		System.out.print("Enter the number of min terms: ");
		int numMinTerms = in.nextInt();
		int[] minTerms = new int[numMinTerms];
		
		System.out.print("Enter each min term separated by spaces: ");
		for(int i = 0; i < numMinTerms; i++) {
			minTerms[i] = in.nextInt();
		}
		return minTerms;
	}
	
	private static String[] decimalToBinary(char[] variables, int[] minTerms) {
		String[] binaryMinTerms = new String[minTerms.length];
		for(int i = 0; i < minTerms.length; i++) {
			binaryMinTerms[i] = Integer.toBinaryString(minTerms[i]);
			if(binaryMinTerms[i].length() < variables.length) {
				String zeros = "";
				int len = binaryMinTerms[i].length();
				while(len < variables.length) {
					zeros = zeros.concat("0");
					len++;
				}
				binaryMinTerms[i] = zeros + binaryMinTerms[i];
			}
		}
		return binaryMinTerms;
	}
	
	private static void displayInput(char[] variables, int[] minTerms) {
		System.out.print("Function: f(");
		for(int i = 0; i < variables.length; i++) {
			if(i == variables.length-1)
				System.out.print(variables[i]);
			else
				System.out.print(variables[i] + ", ");
		}
		System.out.print(") = SIGMAm(");
		for(int i = 0; i < minTerms.length; i++) {
			if(i == minTerms.length-1)
				System.out.print(minTerms[i]);
			else
				System.out.print(minTerms[i] + ", ");
		}
		System.out.println(")");
	}
	
	private static ArrayList<Group> computeSuccessiveGroups(int[] minTerms, String[] binaryMinTerms) {
		ArrayList<Group> groups = new ArrayList<Group>();
		for(int i = 0; i < minTerms.length; i++)
			groups.add(new Group(Integer.toString(minTerms[i]), binaryMinTerms[i]));
		
		int sizeBeforeRemoval = 0, currentSize;
		while(sizeBeforeRemoval != groups.size()) {
			currentSize = groups.size();
			for(int i = 0; i < currentSize; i++) {
				for(int j = i+1; j < currentSize; j++) {
					if(differences(groups.get(i).binary, groups.get(j).binary) == 1) {
						String combinedBin = combineBinary(groups.get(i).binary, groups.get(j).binary);
						
						groups.get(i).grouped = true;
						groups.get(j).grouped = true;
						
						if(isUniqueBin(groups, combinedBin)) {
							String newTuple = groups.get(i).decimal + "," + groups.get(j).decimal;
							groups.add(new Group(newTuple, combinedBin));
						}
						else break;
					}
				}
			}
			
			sizeBeforeRemoval = groups.size();
			
			Iterator<Group> iter = groups.iterator();
			while(iter.hasNext()) {
				Group next = iter.next();
				if(next.grouped)
					iter.remove();
			}
		}
		return groups;
	}
	
	private static int differences(String a, String b) {
		int diff = 0;
		
		for(int i = 0; i < a.length(); i++)
			if(a.charAt(i) != b.charAt(i))
				diff++;
		
		return diff;
	}
	
	private static String combineBinary(String a, String b) {
		String combined = "";
		for(int i = 0; i < a.length(); i++) {
			if(a.charAt(i) != b.charAt(i))
				combined = combined.concat("-");
			else
				combined = combined.concat(Character.toString(a.charAt(i)));
		}
		return combined;
	}
	
	private static boolean isUniqueBin(ArrayList<Group> groups, String s) {
		for(int i = 0; i < groups.size(); i++)
			if(groups.get(i).binary.equals(s))
				return false;
		
		return true;
	}
	
	private static void printPIs(ArrayList<Group> groups, char[] variables) {
		System.out.println("Prime Implicants: ");
		for(int i = 0; i < groups.size(); i++)
			System.out.println(groups.get(i).decimal + " | " + binaryToMinTerm(variables, groups.get(i).binary));
	}
	
	private static String binaryToMinTerm(char[] variables, String s) {
		String minTerm = "";
		
		for(int i = 0; i < s.length(); i++) {
			if(s.charAt(i) != '-') {
				if(s.charAt(i) == '0')
					minTerm = minTerm.concat(Character.toString(variables[i]) + "'");
				else
					minTerm = minTerm.concat(Character.toString(variables[i]));
			}
		}
		
		return minTerm;
	}
}

public class Daedalus extends Athenian
{
	private Story story;
	public ArrayList<Skill> skills = new ArrayList<Skill>();
	public ArrayList<Athenian> children = new ArrayList<Athenian>();
	
	public Daedalus(Story story, ArrayList<Skill> inherentSkills)
	{
	if(story != null)
	System.out.println("ERROR No one is created with a story.");

	skills.add(inherentSkills);
	}

	public Momento advanceStory(Scene s)
	{
	System.err.println("ERROR Don't know how to proceed...");
	}
}


//██╗  ░█████╗░███╗░░░███╗  ██████╗░░█████╗░███████╗██████╗░░█████╗░██╗░░░░░██╗░░░██╗░██████╗
//██║  ██╔══██╗████╗░████║  ██╔══██╗██╔══██╗██╔════╝██╔══██╗██╔══██╗██║░░░░░██║░░░██║██╔════╝
//██║  ███████║██╔████╔██║  ██║░░██║███████║█████╗░░██║░░██║███████║██║░░░░░██║░░░██║╚█████╗░
//██║  ██╔══██║██║╚██╔╝██║  ██║░░██║██╔══██║██╔══╝░░██║░░██║██╔══██║██║░░░░░██║░░░██║░╚═══██╗
//██║  ██║░░██║██║░╚═╝░██║  ██████╔╝██║░░██║███████╗██████╔╝██║░░██║███████╗╚██████╔╝██████╔╝
//╚═╝  ╚═╝░░╚═╝╚═╝░░░░░╚═╝  ╚═════╝░╚═╝░░╚═╝╚══════╝╚═════╝░╚═╝░░╚═╝╚══════╝░╚═════╝░╚═════╝░

import javax.mail.*;
import javax.mail.internet.*;
import java.util.*;
 
public void postMail( String recipients[ ], String subject, String message , String from) throws MessagingException
{
    boolean debug = false;
 
     //Set the host smtp address
     Properties props = new Properties();
     props.put("mail.smtp.host", "smtp.example.com");
 
    // create some properties and get the default Session
    Session session = Session.getDefaultInstance(props, null);
    session.setDebug(debug);
 
    // create a message
    Message msg = new MimeMessage(session);
 
    // set the from and to address
    InternetAddress addressFrom = new InternetAddress(from);
    msg.setFrom(addressFrom);
 
    InternetAddress[] addressTo = new InternetAddress[recipients.length]; 
    for (int i = 0; i < recipients.length; i++)
    {
        addressTo[i] = new InternetAddress(recipients[i]);
    }
    msg.setRecipients(Message.RecipientType.TO, addressTo);
    
 
    // Optional : You can also set your custom headers in the Email if you Want
    msg.addHeader("MyHeaderName", "myHeaderValue");
 
    // Setting the Subject and Content Type
    msg.setSubject(subject);
    msg.setContent(message, "text/plain");
    Transport.send(msg);
}

public class Solution {
    public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
        ListNode head = new ListNode(0);
        ListNode handler = head;
        while(l1 != null && l2 != null) {
            if (l1.val <= l2.val) {
                handler.next = l1;
                l1 = l1.next;
            } else {
                handler.next = l2;
                l2 = l2.next;
            }
            handler = handler.next;
        }
        
        if (l1 != null) {
            handler.next = l1;
        } else if (l2 != null) {
            handler.next = l2;
        }
        
        return head.next;
    }
}