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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		var h1=new int[s[0]][];
		var h2=new int[s[0]][];
		var bs=new Bitset[s[0]][];
		for(int i = 0;i<s[0];i++) {
			h1[i]=sc.Ia;
			bs[i]=new Bitset[s[1]];
		}
		for(int i = 0;i<s[0];i++) {
			h2[i]=sc.Ia;
		}
		int o=100*100*2;
		for(int i = 0;i<s[0];i++) {
			for(int j = 0;j<s[1];j++) {
				bs[i][j]=new Bitset(o*2);
				if(i==0&&j==0){
					bs[i][j][o]=1;
					bs[i][j]>>=Abs(h1[i][j]-h2[i][j]);
					continue;
				}
				if(i!=0){
					bs[i][j]|=bs[i-1][j]<<Abs(h1[i][j]-h2[i][j]);
					bs[i][j]|=bs[i-1][j]>>Abs(h1[i][j]-h2[i][j]);
				}
				if(j!=0){
					bs[i][j]|=bs[i][j-1]<<Abs(h1[i][j]-h2[i][j]);
					bs[i][j]|=bs[i][j-1]>>Abs(h1[i][j]-h2[i][j]);
				}
			}
		}
		int ans=int.MaxValue;
		for(int i = 0;i<o*2;i++) {
			if(bs[s[0]-1][s[1]-1][i]==1){
				ans=Min(ans,Abs(o-i));
			}
		}
		Console.WriteLine("{0}",ans);
	}
}
public class Bitset{
	public int n,l;
	public ulong[] he;
	public Bitset(int n){
		this.n=n;
		l=(n>>6)+1;
		he=new ulong[l];
	}
	public Bitset(int n,long a){
		this.n=n;
		l=(n>>6)+1;
		he=new ulong[l];
		he[0]=(ulong)a;
	}
	public Bitset(int n,bool b){
		this.n=n;
		l=(n>>6)+1;
		he=new ulong[l];
		int y=n%64;
		if(y==0){for(int i = 0;i<l;i++) {he[i]=ulong.MaxValue;}}
		else{
			for(int i = 0;i<l-1;i++) {he[i]=ulong.MaxValue;}
			he[l-1]=(1UL<<y)-1;
		}
	}
	public int this[int i]{
		set{he[i>>6]=(he[i>>6]&(ulong.MaxValue^(1UL<<i)))|((ulong)value<<i);}
		get{return (int)((he[i>>6]>>i)&1);}
	}
	public static Bitset operator&(Bitset a,Bitset b){
		Bitset c=new Bitset(a.n);
		int d=Math.Min(a.l,b.l);
		for(int i=0;i<d;i++){c.he[i]=a.he[i]&b.he[i];}
		return c;
	}
	public static Bitset operator|(Bitset a,Bitset b){
		Bitset c;
		if(a.l<b.l){c=a;a=b;b=c;}
		c=new Bitset(a.n);
		int i=0;
		for(;i<b.l;i++){c.he[i]=a.he[i]|b.he[i];}
		for(;i<a.l;i++){c.he[i]=a.he[i];}
		return c;
	}
	public static Bitset operator^(Bitset a,Bitset b){
		Bitset c;
		if(a.l<b.l){c=a;a=b;b=c;}
		c=new Bitset(a.n);
		int i=0;
		for(;i<b.l;i++){c.he[i]=a.he[i]^b.he[i];}
		for(;i<a.l;i++){c.he[i]=a.he[i];}
		return c;
	}
	public static Bitset operator<<(Bitset a,int b){
		Bitset c=new Bitset(a.n);
		if(b>a.l<<6){return c;}
		int d=(b+63)>>6;
		if(b%64==0){for(int i=a.l-1;i>=d;i--){c.he[i]=a.he[i-d];}}
		else{
			for(int i=a.l-1;i>=d;i--){c.he[i]=(a.he[i-d+1]<<b)|(a.he[i-d]>>(64-b));}
			c.he[d-1]=a.he[0]<<b;
		}
		return c;
	}
	public static Bitset operator>>(Bitset a,int b){
		Bitset c=new Bitset(a.n);
		if(b>a.l<<6){return c;}
		int d=(b+63)>>6;
		if(b%64==0){for(int i=0;i+d<c.l;i++){c.he[i]=a.he[i+d];}}
		else{
			for(int i=0;i+d<c.l;i++){c.he[i]=(a.he[i+d-1]>>b)|(a.he[i+d]<<(64-b));}
			c.he[c.l-d]=a.he[c.l-1]>>b;
		}
		return c;
	}
	public static bool operator==(Bitset a,Bitset b){
		int mx=Max(a.l,b.l),mn=Min(a.l,b.l);
		for(int i=0;i<mn;i++){if(a.he[i]!=b.he[i]){return false;}}
		if(a.l>b.l){for(int i=mn;i<mx;i++){if(a.he[i]!=0){return false;}}}
		else{for(int i=mn;i<mx;i++){if(b.he[i]!=0){return false;}}}
		return true;
	}
	public static bool operator!=(Bitset a,Bitset b){
		int mx=Max(a.l,b.l),mn=Min(a.l,b.l);
		for(int i=0;i<mn;i++){if(a.he[i]!=b.he[i]){return true;}}
		if(a.l>b.l){for(int i=mn;i<mx;i++){if(a.he[i]!=0){return true;}}}
		else{for(int i=mn;i<mx;i++){if(b.he[i]!=0){return true;}}}
		return false;
	}
	public override bool Equals(object obj){return false;}
	public override int GetHashCode(){return 0;}
	public string St(){
		string t="",s;
		for(int i = 0;i<l-1;i++) {
			s=Convert.ToString((long)he[i],2);
			s=(64>s.Length?new string('0',64-s.Length):"")+s;
			t=s+t;
		}
		s=Convert.ToString((long)he[l-1],2);
		s=((n%64)>s.Length?new string('0',(n%64)-s.Length):"")+s;
		return s+t;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}