Problem:
Score : 500 points

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.

The square (i, j) has two numbers A_{ij} and B_{ij} written on it.

First, for each square, Takahashi paints one of the written numbers red and the other blue.

Then, he travels from the square (1, 1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.

Let the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1, 1) and (H, W).

Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.

Find the minimum unbalancedness possible.

Constraints

2 \leq H \leq 80

2 \leq W \leq 80

0 \leq A_{ij} \leq 80

0 \leq B_{ij} \leq 80

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W
A_{11} A_{12} \ldots A_{1W}
:
A_{H1} A_{H2} \ldots A_{HW}
B_{11} B_{12} \ldots B_{1W}
:
B_{H1} B_{H2} \ldots B_{HW}

Output

Print the minimum unbalancedness possible.

Sample Input 1

2 2
1 2
3 4
3 4
2 1

Sample Output 1

0

By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.

Sample Input 2

2 3
1 10 80
80 10 1
1 2 3
4 5 6

Sample Output 2

2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map.Entry;

import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {
	
	public static void main(String[] args) throws IOException {	
		try(final Scanner sc = new Scanner(System.in)){
			final int H = sc.nextInt();
			final int W = sc.nextInt();
			
			final int GAP = 100 + 1;
			
			int[][] as = new int[H][W];
			for(int i = 0; i < H; i++) {
				for(int j = 0; j < W; j++) {
					as[i][j] = sc.nextInt();
				}
			}
			
			int[][] bs = new int[H][W];
			for(int i = 0; i < H; i++) {
				for(int j = 0; j < W; j++) {
					bs[i][j] = sc.nextInt();
				}
			}
			
			boolean[][][][] DP = new boolean[H][W][GAP][GAP];
			DP[0][0][0][0] = true;
			
			for(int i = 0; i < H; i++) {
				for(int j = 0; j < W; j++) {
					
					for(int r = 0; r < GAP; r++) {
						for(int b = 0; b < GAP; b++) {
							if(!DP[i][j][r][b]) { continue; }
							
							{
								int next_r = r + as[i][j];
								int next_b = b + bs[i][j];
								final int common = Math.min(next_r, next_b);
								next_r -= common; next_b -= common;
								
								if(next_r < GAP & next_b < GAP) {
									if(i < H - 1) { DP[i + 1][j][next_r][next_b] = true; }
									if(j < W - 1) { DP[i][j + 1][next_r][next_b] = true; }
								}
							}
							{
								int next_r = r + bs[i][j];
								int next_b = b + as[i][j];
								final int common = Math.min(next_r, next_b);
								next_r -= common; next_b -= common;
								
								if(next_r < GAP & next_b < GAP) {
									if(i < H - 1) { DP[i + 1][j][next_r][next_b] = true; }
									if(j < W - 1) { DP[i][j + 1][next_r][next_b] = true; }
								}
							}
						}
					}
				}
			}

			int answer = Integer.MAX_VALUE;
			for(int r = 0; r < GAP; r++) {
				for(int b = 0; b < GAP; b++) {
					if(!DP[H - 1][W - 1][r][b]) { continue; }
					
					{
						int next_r = r + as[H - 1][W - 1];
						int next_b = b + bs[H - 1][W - 1];
						final int common = Math.min(next_r, next_b);
						next_r -= common; next_b -= common;
						
						answer = Math.min(answer, Math.abs(next_r - next_b));
					}
					{
						int next_r = r + bs[H - 1][W - 1];
						int next_b = b + as[H - 1][W - 1];
						final int common = Math.min(next_r, next_b);
						next_r -= common; next_b -= common;
						
						answer = Math.min(answer, Math.abs(next_r - next_b));
					}
				}
			}
			
			System.out.println(answer);
		}
	}

	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() throws IOException {
			while(!hasNext()){
				tok = new StringTokenizer(br.readLine());
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}

		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}

		public void close() throws IOException {
			br.close();
		}
	}
}