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 Rust (1.15.1) (judge verdict: Wrong Answer)

// SNIPPET read
pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $t:ty, $words_count:expr, |$words:ident| $read_words:expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize { $words_count }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize { 1 }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
macro_rules! impl_readable_for_ints {
    ( $( $t:ty )* ) => { $(
        impl Readable for $t {
            type Output = Self;
            fn words_count() -> usize { 1 }
            fn read_words(words: &[&str]) -> Result<$t, String> {
                use std::str::FromStr;
                <$t>::from_str(words[0]).map_err(|_| {
                    format!("cannot parse `{}` as {}", words[0], stringify!($t))
                })
            }
        }
    )* };
}
impl_readable_for_ints!(i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64);
macro_rules! define_one_origin_int_types {
    ( $new_t:ident $int_t:ty ) => {
        #[allow(non_camel_case_types)]
        pub struct $new_t;
        impl Readable for $new_t {
            type Output = $int_t;
            fn words_count() -> usize { 1 }
            fn read_words(words: &[&str]) -> Result<Self::Output, String> {
                <$int_t>::read_words(words).map(|n| n-1)
            }
        }
    };
    ( $new_t:ident $int_t:ty; $( $inner_new_t:ident $inner_int_t:ty );* ) => {
        define_one_origin_int_types!($new_t $int_t);
        define_one_origin_int_types!($($inner_new_t $inner_int_t);*);
    };
}
define_one_origin_int_types!(u8_ u8; u16_ u16; u32_ u32; u64_ u64; usize_ usize);
macro_rules! impl_readable_for_tuples {
    ( $t:ident $var:ident ) => ();
    ( $t:ident $var:ident; $( $inner_t:ident $inner_var:ident );* ) => {
        impl_readable_for_tuples!($($inner_t $inner_var);*);
        impl<$t: Readable, $($inner_t: Readable),*> Readable
            for ($t, $($inner_t),*)
        {
            type Output = ( <$t>::Output, $(<$inner_t>::Output),* );
            fn words_count() -> usize {
                let mut n = <$t>::words_count();
                $(
                    n += <$inner_t>::words_count();
                )*
                n
            }
            #[allow(unused_assignments)]
            fn read_words(words: &[&str]) ->
                Result<Self::Output, String>
            {
                let mut start = 0;
                let $var = <$t>::read_words(
                    &words[start .. start+<$t>::words_count()]
                )?;
                start += <$t>::words_count();
                $(
                    let $inner_var =
                        <$inner_t>::read_words(
                            &words[start .. start+<$inner_t>::words_count()]
                        )?;
                    start += <$inner_t>::words_count();
                )*
                Ok(( $var, $($inner_var),* ))
            }
        }
    };
}
impl_readable_for_tuples!(T8 x8; T7 x7; T6 x6; T5 x5; T4 x4; T3 x3; T2 x2; T1 x1);
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!("line `{}` has {} words, expected {}",
                               line, words.len(), T::words_count()));
        }
        T::read_words(&words)
    }
}
macro_rules! impl_readable_from_line_for_tuples_with_from_iterator {
    ( $u:ident : $( + $bound:path )* => $seq_in:ty, $seq_out:ty; $t:ident $var:ident ) => {
        impl<$u: Readable> ReadableFromLine for $seq_in
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = $seq_out;
            fn read_line(line: &str) -> Result<$seq_out, String> {
                let n = $u::words_count();
                let words = split_into_words(line);
                if words.len() % n != 0 {
                    return Err(format!("line `{}` has {} words, expected multiple of {}",
                                       line, words.len(), n));
                }
                let mut result = Vec::new();
                for chunk in words.chunks(n) {
                    match $u::read_words(chunk) {
                        Ok(v) => result.push(v),
                        Err(msg) => {
                            let flagment_msg = if n == 1 {
                                format!("word {}", result.len())
                            } else {
                                let l = result.len();
                                format!("words {}-{}", n*l + 1, (n+1) * l)
                            };
                            return Err(format!(
                                "{} of line `{}`: {}", flagment_msg, line, msg
                            ));
                        }
                    }
                }
                Ok(result.into_iter().collect())
            }
        }
        impl<T: Readable, $u: Readable> ReadableFromLine for (T, $seq_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = (T::Output, $seq_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let n = T::words_count();
                #[allow(deprecated)]
                let trimmed = line.trim_right_matches('\n');
                let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ').collect();
                if words_and_rest.len() < n {
                    return Err(format!("line `{}` has {} words, expected at least {}",
                                       line, words_and_rest.len(), n));
                }
                let words = &words_and_rest[..n];
                let empty_str = "";
                let rest = words_and_rest.get(n).unwrap_or(&empty_str);
                Ok((T::read_words(words)?, <$seq_in>::read_line(rest)?))
            }
        }
    };
    ( $u:ident : $( + $bound:path )* => $seq_in:ty, $seq_out:ty;
      $t:ident $var:ident, $( $inner_t:ident $inner_var:ident ),+ ) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: $(+ $bound)* => $seq_in, $seq_out; $($inner_t $inner_var),+
        );
        impl<$t: Readable, $($inner_t: Readable),+ , $u: Readable> ReadableFromLine
            for ($t, $($inner_t),+ , $seq_in)
        where
            <$u as Readable>::Output: Sized $(+ $bound)*
        {
            type Output = ($t::Output, $($inner_t::Output),+ , $seq_out);
            fn read_line(line: &str) -> Result<Self::Output, String> {
                let mut n = $t::words_count();
                $(
                    n += $inner_t::words_count();
                )+
                #[allow(deprecated)]
                let trimmed = line.trim_right_matches('\n');
                let words_and_rest: Vec<&str> = trimmed.splitn(n + 1, ' ')
                    .collect();
                if words_and_rest.len() < n {
                    return Err(
                        format!("line `{}` has {} words, expected at least {}",
                                line, words_and_rest.len(), n)
                    );
                }
                let words = &words_and_rest[..n];
                let empty_str = "";
                let rest = words_and_rest.get(n).unwrap_or(&empty_str);
                let ($var, $($inner_var),*) =
                    <($t, $($inner_t),+)>::read_words(words)?;
                Ok(($var, $($inner_var),* , <$seq_in>::read_line(rest)?))
            }
        }
    };
}
#[macro_export]
macro_rules! readable_collection {
    ($u:ident => $collection_in:ty, $collection_out:ty) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: => $collection_in, $collection_out;
            T8 x8, T7 x7, T6 x6, T5 x5, T4 x4, T3 x3, T2 x2, T1 x1
        );
    };
    ($u:ident : $( $bound:path ),* => $collection_in:ty, $collection_out:ty) => {
        impl_readable_from_line_for_tuples_with_from_iterator!(
            $u: $(+ $bound)* => $collection_in, $collection_out;
            T8 x8, T7 x7, T6 x6, T5 x5, T4 x4, T3 x3, T2 x2, T1 x1
        );
    }
}
readable_collection!(U => Vec<U>, Vec<U::Output>);
readable_collection!(
    U => std::collections::VecDeque<U>, std::collections::VecDeque<U::Output>
);
readable_collection!(
    U: Eq, std::hash::Hash => std::collections::HashSet<U>, std::collections::HashSet<U::Output>
);
readable_collection!(
    U: Ord => std::collections::BTreeSet<U>, std::collections::BTreeSet<U::Output>
);
readable_collection!(
    U: Ord => std::collections::BinaryHeap<U>, std::collections::BinaryHeap<U::Output>
);
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules! read {
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };
    ( $pat:pat = $t:ty ) => {
        let $pat = read::<$t>();
    };
    ( $( $pat:pat = $t:ty ),+ ) => {
        read!(($($pat),*) = ($($t),*));
    };
}
#[macro_export]
macro_rules! readls {
    ( $( $pat:pat = $t:ty ),+ ) => {
        $(
            read!($pat = $t);
        )*
    };
}
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin.lock().lines().map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    result
}
#[macro_export]
macro_rules! readx_loop {
    ( |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            for line in stdin.lock().lines() {
                let line = line.expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( |$($pat:pat = $t:ty),*| $body:expr ) => {
        readx_loop!(|($($pat),*) = ($($t),*)| $body);
    };
}
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin.lock().lines().take(n).map(|line_result| {
        let line = line_result.expect("read from stdin failed");
        T::read_line(&line).unwrap()
    }).collect();
    if result.len() < n {
        panic!("expected reading {} lines, but only {} lines are read",
               n, result.len());
    }
    result
}
#[macro_export]
macro_rules! readn_loop {
    ( $n:expr, |$pat:pat = $t:ty| $body:expr ) => {
        {
            use std::io::BufRead;
            let stdin = std::io::stdin();
            let mut lock = stdin.lock();
            for _ in 0..$n {
                let mut line = String::new();
                lock.read_line(&mut line).expect("read from stdin failed");
                let $pat = <$t>::read_line(&line).unwrap();
                $body
            }
        }
    };
    ( $n:expr, |$($pat:pat = $t:ty),*| $body:expr ) => {
        readn_loop!($n, |($($pat),*) = ($($t),*)| $body);
    };
}
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

// SNIPPET dbg
#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    () => {
        {
            use std::io::{self, Write};
            writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
        }
    };
    ($e: expr) => {
        {
            use std::io::{self, Write};
            let result = $e;
            writeln!(io::stderr(), "{}: {} = {:?}",
                     line!(), stringify!($e), result)
                .unwrap();
            result
        }
    }
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    () => {};
    ($e: expr) => {
        { $e }
    }
}

// END SNIPPETS

const MIN: i16 = -6400;
const MAX: i16 = 6400;

fn set(dest: &mut [bool], src: &[bool], d: i16) {
    let d = d.abs();
    for i in d..(-MIN+MAX+1) {
        if src[i as usize] {
            dbg!(i-d);
            dest[(i-d) as usize] = true;
        }
    }
    for i in 0..(-MIN+MAX+1-d) {
        if src[i as usize] {
            dbg!(i+d);
            dest[(i+d) as usize] = true;
        }
    }
}

fn main() {
    read!(h = usize, w = usize);
    let mut board = vec![vec![0; w+1]];
    for _ in 0..h {
        read!(mut row = Vec<i16>);
        row.insert(0, 0);
        board.push(row);
    }
    for y in 0..h {
        read!(row = Vec<i16>);
        for x in 0..w {
            board[y+1][x+1] -= row[x];
        }
    }
    dbg!(&board);

    let mut init = vec![false; (MAX-MIN+1) as usize];
    init[(-MIN) as usize] = true;
    let mut sets = vec![vec![init.clone(); w+1]; 1];
    for _ in 1..h+1 {
        sets.push(vec![init.clone()]);
    }
    for y in 1..h+1 {
        for x in 1..w+1 {
            dbg!((x, y, board[y][x]));
            let mut cell = vec![false; (MAX-MIN+1) as usize];
            set(&mut cell, &sets[y-1][x], board[y][x]);
            set(&mut cell, &sets[y][x-1], board[y][x]);
            sets[y].push(cell);
        }
    }

    let ans = (MIN..).zip(sets[h][w].iter())
        .filter(|&(_, &b)| b).map(|(d, _)| d.abs()).min().unwrap();
    println!("{}", ans);
}