package v3;

import java.io.File;
import java.io.FileNotFoundException;
import java.util.Scanner;

public class hw2 {
	private static int inLength, numIn, numOut, numTrues;
	private static int[] onesCount, groups;
	private static int[][] ins, outs, holdOnes, ansOnes;
	private static boolean reduced;
	private static boolean[][] trues;
	public static void main(String[] args) {
		try {
			Scanner s = new Scanner(new File("input.txt"));
			numIn = s.nextInt();
			if(numIn > 100) {
				System.out.println("Sorry, that input amount is too high, The max is: 100");
				System.exit(0);
			}
			inLength = (int) Math.pow(2, numIn);
			numOut = s.nextInt();
			if(numOut > 26) {
				System.out.println("Sorry, that output amount is too high, The max is: 226");
				System.exit(0);
			}
			ins = new int[numIn][inLength];
			outs = new int[numOut][inLength];
			fillIn();
			fillOut(s);
			for(int i = 0; i < numOut; i++) {
				pullOnes(i);
				groupIt(holdOnes, numIn);
				System.out.println(((char)('A'+i))+" = "+printResult(i, ansOnes));
			}
			//printData();
			s.close();
		} catch (FileNotFoundException e) {
			System.out.println("Sorry, this file could not be found");
		}
	}

	private static void groupIt(int[][] hO, int nums) {
		int totalCount = 0;
		for(int i = 0; i < hO.length; i++) {
			int counter = 0;
			for(int j = 0; j < numIn; j++) {
				if(hO[i][j] == 1) {
					counter++;
					totalCount++;
				}
			}
		}
		ansOnes = new int[totalCount][numIn];
		int truePos = 0;
		int whatGroup = 0;

		for(int i = 0; i < hO.length; i++) {
			for(int j = i; j < hO.length; j++) {
				int counter = 0;
				for(int k = 0; k < numIn; k++) {
					if(hO[i][k] != hO[j][k]) {
						counter++;
					}
				}
				if(counter == 1) {
					ansOnes = mergeIt(hO, ansOnes, i, j, truePos);
					truePos++;
				}
			}
		}
		if(truePos < ansOnes.length) {
			for(int i = truePos; i < ansOnes.length; i++) {
				for(int j = truePos; j < numIn; j++) {
					ansOnes[i][j] = 3;
				}
			}
		}
		nums--;
		if(nums > 2) {
			groupIt(ansOnes, nums);
		}
	}

	private static int[][] mergeIt(int[][] hO, int[][] h1, int p1, int p2, int pos) {
		for(int i = 0; i < numIn; i++) {
			if(hO[p1][i] == hO[p2][i]) {
				h1[pos][i] = hO[p1][i];
			} else {
				h1[pos][i] = 2;
			}
		}
		return h1;
	}

	private static void pullOnes(int pos) {
		holdOnes = new int[onesCount[pos]][numIn];
		int counter = 0;
		for(int i = 0; i < inLength; i++) {
			if(outs[pos][i] == 1) {
				for(int j = 0; j < numIn; j++) {
					holdOnes[counter][j] = ins[j][i];
				}
				counter++;
			}
		}
	}

	private static String printResult(int pos, int[][] arr) {
		String result = "";
		boolean last = false;
		for(int i = 0; i < arr.length; i++) {
			result += "(";
			boolean first = true;
			for (int j = 0; j < arr[i].length; j++) {
				if (arr[i][j] == 1) {
					if (j < 10) {
						if (first) {
							result += "IN0" + j;
							first = false;
						} else {
							result += " * IN0" + j;
						}
					} else {
						if (first) {
							result += "IN" + j;
							first = false;
						} else {
							result += "* IN" + j;
						}
					}
				} else if (arr[i][j] == 0) {
					if (j < 10) {
						if (first) {
							result += "IN0" + j + "'";
							first = false;
						} else {
							result += " * IN0" + j + "'";
						}
					} else {
						if (first) {
							result += "IN" + j + "'";
							first = false;
						} else {
							result += "* IN" + j + "'";
						}
					}
				}
				if (i == arr.length - 1 && j == arr[i].length - 1) {
					last = true;
				}
			}
			result += ")";
			if (!last) {
				result += " + ";
			}
		}
		return result;
	}
	/*
	private static void trueReduce(int length) {
		reduced = false;
		for(int i = 0; i < length; i++) {
			for(int j = 0; j < length; j++) {
				int c1 = 0, c2 = 0;
				if(trues[i][j]) {
					for(int k = 0; k < length; k++) {
						if(trues[i][j] == trues[i][k] && j != k) {
							c1 = 1;
						}
					}
					for(int k = 0; k < length; k++) {
						if(trues[i][j] == trues[i][k] && i != k) {
							c2 = 1;
						}
					}
					if(c1 + c2 == 2) {
						reduced = true;
						trues[i][j] = false;
						numTrues--;
					}
				}
			}
		}
	}

	private static void duplicateReduce(int length) {
		System.out.println(numTrues + " " + numIn);
		ansOnes = new int[numTrues][numIn];
		int count = 0;
		for(int i = 0; i < length; i++) {
			for(int j = 0; j < length; j++) {
				if(trues[i][j]) {
					for(int k = 0; k < numIn; k++) {
						if (holdOnes[i][k] != holdOnes[j][k]) {
							ansOnes[count][k] = 2;
						} else {
							ansOnes[count][k] = holdOnes[i][k];
						}
						System.out.print(ansOnes[count][k] + " ");
					}
					count++;
					System.out.println();
				}
			}
		}
	}*/

	private static void placeTrue(int length) {
		trues = new boolean[20][30];
		for(int i = 0; i < length; i++) {
			for(int j = 0; j < length; j++) {
				trues[i][j] = false;
			}
		}
		numTrues = 0;
		for(int i = 0; i < length; i++) {
			for(int j = i; j < length; j++) {
				int numFalse = 0;
				for(int k = 0; k < numIn; k++) {
					if(holdOnes[i][k] != holdOnes[j][k]) {
						numFalse++;
					}
				}
				if(numFalse == 1) {
					trues[i][j] = true;
					numTrues++;
				}
			}
		}

	}

	private static void fillOut(Scanner s) {
		onesCount = new int[numOut];
		for (int i = 0; i < numOut; i++) {
			onesCount[i] = 0;
		}
		for (int j = 0; j < inLength; j++) {
			for (int i = 0; i < numOut; i++) {
				int num = s.nextInt();
				if (num == 1) {
					onesCount[i]++;
				}
				outs[i][j] = num;
			}
		}
	}

	private static void fillIn() {
		for(int i = 0; i < numIn; i++) {
			int fill = (int)(inLength/Math.pow(2, i+1));
			boolean tf = true;
			for(int j = 0; j < inLength; j++) {
				if(j%fill == 0 && j > 0) {
					tf = !tf;
				}
				if(tf) {
					ins[i][j] = 0;
				} else {
					ins[i][j] = 1;
				}
			}
		}
	}

	private static void printData() {
		System.out.println();
		System.out.println("Truth Table:");
		for(int j = 0; j < inLength; j++) {
			for(int i = 0; i < numIn; i++) {
				System.out.print(ins[i][j] + " ");
			}
			for(int i = 0; i < numOut; i++) {
				System.out.print(outs[i][j] + " ");
			}
			System.out.println();
		}
	}

}