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 Factorial
{
	public static void main(String[] args)
	{	final int NUM_FACTS = 100;
		for(int i = 0; i < NUM_FACTS; i++)
			System.out.println( i + "! is " + factorial(i));
	}
	
	public static int factorial(int n)
	{	int result = 1;
		for(int i = 2; i <= n; i++)
			result *= i;
		return result;
	}
}

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);
}

import java.util.Arrays;

public class LongestIncreasingSubsequence {
    public int lengthOfLIS(int[] nums) {
        if (nums.length == 0) {
            return 0;
        }

        int[] dp = new int[nums.length];
        Arrays.fill(dp, 1); // Initialize all elements in dp array to 1, as each element itself is a valid subsequence of length 1.

        int maxLength = 1; // Initialize the maximum length to 1, considering a single element as the sequence.

        for (int i = 1; i < nums.length; i++) {
            for (int j = 0; j < i; j++) {
                if (nums[i] > nums[j]) {
                    dp[i] = Math.max(dp[i], dp[j] + 1); // If nums[i] is greater than nums[j], update the longest subsequence length ending at i.
                }
            }
            maxLength = Math.max(maxLength, dp[i]); // Update the maximum length if needed.
        }

        return maxLength;
    }

    public static void main(String[] args) {
        LongestIncreasingSubsequence lis = new LongestIncreasingSubsequence();
        int[] nums = {10, 9, 2, 5, 3, 7, 101, 18};
        int result = lis.lengthOfLIS(nums);
        System.out.println("Length of the Longest Increasing Subsequence: " + result); // Output: 4
    }
}

public class UserService {

  private UserRepository userRepository;

  public UserService(UserRepository userRepository) {
    this.userRepository = userRepository;
  }

  public User getUserById(long id) {
    try {
      return userRepository.getUserById(id);
    } catch (Exception e) {
      // Log the exception here
      System.out.println("An error occurred while fetching the user: " + e.getMessage());
      return null;
    }
  }
}

public class UserRepository {

  public User getUserById(long id) throws Exception {
    // Database query to fetch the user
    if (id < 0) {
      throw new Exception("Invalid user id");
    }
    // Return the user object
    return new User(id, "John Doe");
  }
}

public class User {

  private long id;
  private String name;

  public User(long id, String name) {
    this.id = id;
    this.name = name;
  }

  public long getId() {
    return id;
  }

  public String getName() {
    return name;
  }
}

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);
}