Problem:
Score : 400 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i,j) be the square at the i-th row from the top and the j-th column from the left.

These squares have to be painted in one of the C colors from Color 1 to Color C. Initially, (i,j) is painted in Color c_{i,j}.

We say the grid is a good grid when the following condition is met for all i,j,x,y satisfying 1 \leq i,j,x,y \leq N:

If (i+j) \% 3=(x+y) \% 3, the color of (i,j) and the color of (x,y) are the same.

If (i+j) \% 3 \neq (x+y) \% 3, the color of (i,j) and the color of (x,y) are different.

Here, X \% Y represents X modulo Y.

We will repaint zero or more squares so that the grid will be a good grid.

For a square, the wrongness when the color of the square is X before repainting and Y after repainting, is D_{X,Y}.

Find the minimum possible sum of the wrongness of all the squares.

Constraints

1 \leq N \leq 500

3 \leq C \leq 30

1 \leq D_{i,j} \leq 1000 (i \neq j),D_{i,j}=0 (i=j)

1 \leq c_{i,j} \leq C

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N C
D_{1,1} ... D_{1,C}
:
D_{C,1} ... D_{C,C}
c_{1,1} ... c_{1,N}
:
c_{N,1} ... c_{N,N}

Output

If the minimum possible sum of the wrongness of all the squares is x, print x.

Sample Input 1

2 3
0 1 1
1 0 1
1 4 0
1 2
3 3

Sample Output 1

3

Repaint (1,1) to Color 2. The wrongness of (1,1) becomes D_{1,2}=1.

Repaint (1,2) to Color 3. The wrongness of (1,2) becomes D_{2,3}=1.

Repaint (2,2) to Color 1. The wrongness of (2,2) becomes D_{3,1}=1.

In this case, the sum of the wrongness of all the squares is 3.

Note that D_{i,j} \neq D_{j,i} is possible.

Sample Input 2

4 3
0 12 71
81 0 53
14 92 0
1 1 2 1
2 1 1 2
2 2 1 3
1 1 2 2

Sample Output 2

428

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp::*;
use std::io::*;
use std::str::FromStr;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = AtRead::from(i);
    let (n, c) = i.read2::<usize, usize>();
    let mut d = Vec::new();
    for _ in 0..c {
        d.push(i.read_vec::<usize>(c));
    }
    let mut x = Vec::new();
    for _ in 0..n {
        let mut xi = i.read_vec::<usize>(n);
        for xii in xi.iter_mut() {
            *xii -= 1;
        }
        x.push(xi);
    }
    writeln!(o, "{}", solve(&d, &x)).unwrap();
}
fn solve(d: &[Vec<usize>], c: &[Vec<usize>]) -> usize {
    let mut d_sums = vec![vec![0; d.len()]; 3];
    for ci in 0..d.len() {
        for x in 0..c.len() {
            for y in 0..c.len() {
                d_sums[(x + y) % 3][ci] += d[c[x][y]][ci];
            }
        }
    }
    let mut result = usize::max_value();
    for i0 in 0..d.len() {
        for i1 in 0..d.len() {
            if i1 == i0 {
                continue;
            }
            for i2 in 0..d.len() {
                if i2 == i0 || i2 == i1 {
                    continue;
                }
                result = min(result, d_sums[0][i0] + d_sums[1][i1] + d_sums[2][i2]);
            }
        }
    }
    result
}

mod utils {
    #![allow(dead_code)]
    use super::*;
    use std::ops::*;

    pub struct AtRead<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                $(
                    let $v = next(i);
                )*
                ($($v),*)
            }
        };
    }

    impl<R: BufRead> AtRead<R> {
        pub fn from(r: R) -> Self {
            AtRead {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_line().parse().ok().unwrap()
        }
        fn_read! { read2(v1: T1, v2: T2) }
        fn_read! { read3(v1: T1, v2: T2, v3: T3) }
        fn_read! { read4(v1: T1, v2: T2, v3: T3, v4: T4) }
        fn_read! { read5(v1: T1, v2: T2, v3: T3, v4: T4, v5: T5) }

        pub fn read_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            self.read_line()
                .split(' ')
                .take(n)
                .map(|x| x.parse().ok().unwrap())
                .collect()
        }
        pub fn read_array<A: AsMut<[T]> + Default, T: FromStr>(&mut self) -> A {
            let mut a: A = Default::default();
            {
                let a: &mut [T] = a.as_mut();
                let i = &mut self.read_line().split(' ');
                for n in 0..a.len() {
                    a[n] = next(i);
                }
            }
            a
        }
    }

    fn next<'a, T: FromStr, I: std::iter::Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }

    #[derive(Debug, Clone, Copy)]
    pub struct ModInt(pub usize);

    const MOD_BASE: usize = 1000000007;
    const MOD_INV_POW: usize = 1000000005;

    impl ModInt {
        pub fn new(n: usize) -> Self {
            ModInt(n % MOD_BASE)
        }
        pub fn pow(self, mut exp: usize) -> Self {
            let mut b = self;
            let mut r = ModInt(1);
            while exp != 0 {
                if exp % 2 == 1 {
                    r *= b;
                }
                exp /= 2;
                b = b * b;
            }
            r
        }
        pub fn inverse_element(self) -> Self {
            self.pow(MOD_INV_POW)
        }
    }

    macro_rules! ModInt_op {
        (($ot:ident, $f:ident), ($ot_a:ident, $f_a:ident), $($rhs:ty, $e:expr,)*) => {
            $(
            impl $ot<$rhs> for ModInt {
                type Output = Self;
                fn $f(self, rhs: $rhs) -> Self {
                    Self::new(($e)(self, rhs))
                }
            }
            impl $ot_a<$rhs> for ModInt {
                fn $f_a(&mut self, rhs: $rhs) {
                    *self = Self::new(($e)(*self, rhs))
                }
            }
            )*
        }
    }

    ModInt_op!(
        (Add, add),
        (AddAssign, add_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 + r.0,
        usize,
        |l: ModInt, r: usize| l.0 + r,
    );

    ModInt_op!(
        (Mul, mul),
        (MulAssign, mul_assign),
        ModInt,
        |l: ModInt, r: ModInt| l.0 * r.0,
        usize,
        |l: ModInt, r: usize| l.0 * r,
    );

    ModInt_op!(
        (Sub, sub),
        (SubAssign, sub_assign),
        ModInt,
        |l: ModInt, r: ModInt| MOD_BASE + l.0 - r.0,
        usize,
        |l: ModInt, r: usize| MOD_BASE + l.0 - r,
    );

    // std::cmp::Reverseと同じ
    #[derive(PartialEq, Eq)]
    pub struct RevCmp<T>(pub T);

    impl<T: PartialOrd> PartialOrd for RevCmp<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }
    impl<T: Ord> Ord for RevCmp<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    pub struct PascalsTriangle<T> {
        buf: Vec<T>,
        n: usize,
    }

    impl<T: One> PascalsTriangle<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangle {
                buf: vec![T::one()],
                n: 1,
            };
            while s.n <= n {
                let i = s.buf.len() - s.n;
                s.buf.push(T::one());
                for m in 1..s.n {
                    let v = s.buf[i + m - 1] + s.buf[i + m];
                    s.buf.push(v);
                }
                s.buf.push(T::one());
                s.n += 1;
            }
            s
        }
        pub fn get(&mut self, n: usize, m: usize) -> T {
            debug_assert!(n <= self.n);
            debug_assert!(m <= n);
            self.buf[n * (n + 1) / 2 + m]
        }
    }

    pub struct PascalsTriangleIter<T> {
        buf: Vec<T>,
    }
    impl<T: One> PascalsTriangleIter<T> {
        pub fn new(n: usize) -> Self {
            let mut s = PascalsTriangleIter {
                buf: Vec::with_capacity(n + 1),
            };
            for _ in 0..n + 1 {
                s.next();
            }
            s
        }
        pub fn next(&mut self) {
            for i in (1..self.buf.len()).rev() {
                self.buf[i] = self.buf[i] + self.buf[i - 1];
            }
            self.buf.push(T::one());
        }
        pub fn get(&self) -> &[T] {
            &self.buf
        }
    }

    pub struct ModIntFacts {
        f: Vec<ModInt>,
        rf: Vec<ModInt>,
    }
    impl ModIntFacts {
        pub fn new(n: usize) -> Self {
            let mut s = ModIntFacts {
                f: vec![ModInt(0); n + 1],
                rf: vec![ModInt(0); n + 1],
            };

            let v = ModInt(1);
            s.f[0] = v;
            for i in 1..n + 1 {
                s.f[i] = s.f[i - 1] * i;
            }
            s.rf[n] = s.f[n].inverse_element();
            for i in (1..n + 1).rev() {
                s.rf[i - 1] = s.rf[i] * i;
            }
            s
        }
        pub fn fact(&self, n: usize) -> ModInt {
            self.f[n]
        }
        pub fn comb(&self, n: usize, c: usize) -> ModInt {
            self.f[n] * self.rf[c] * self.rf[n - c]
        }
    }

    pub trait Zero: Add<Output = Self> + Sized + Copy {
        fn zero() -> Self;
    }
    pub trait One: Zero {
        fn one() -> Self;
    }

    macro_rules! impl_zero {
        ($t:ty, $e:expr) => {
            impl Zero for $t {
                fn zero() -> Self {
                    $e
                }
            }
        }
    }
    macro_rules! impl_one {
        ($t:ty, $e1:expr, $e0:expr) => {
            impl One for $t {
                fn one() -> Self {
                    $e1
                }
            }
            impl_zero!($t, $e0);
        };
    }

    impl_one!(usize, 1, 0);
    impl_one!(u32, 1, 0);
    impl_one!(i32, 1, 0);
    impl_one!(f64, 1.0, 0.0);
    impl_one!(ModInt, ModInt(1), ModInt(0));

    pub trait BinarySearchExt<T> {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize;
        fn lower_bound(&self, x: &T) -> usize;
        fn upper_bound(&self, x: &T) -> usize;
    }
    impl<T: Ord> BinarySearchExt<T> for [T] {
        fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize {
            let mut low = 0;
            let mut high = self.len();
            while low < high {
                let mid = (low + high) / 2;
                if f(&self[mid]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            low
        }
        fn lower_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x <= y)
        }
        fn upper_bound(&self, x: &T) -> usize {
            self.lower_bound_by(|y| x < y)
        }
    }

    pub trait AtSliceExt<T> {
        fn rotate(&mut self, mid: usize);
    }
    impl<T> AtSliceExt<T> for [T] {
        fn rotate(&mut self, mid: usize) {
            {
                let (l, r) = self.split_at_mut(mid);
                l.reverse();
                r.reverse();
            }
            self.reverse()
        }
    }

}