Problem:
Score : 1000 points

Problem Statement

Note the unusual memory limit.

For a rectangular grid where each square is painted white or black, we define its complexity as follows:

If all the squares are black or all the squares are white, the complexity is 0.

Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of the grid, and let c_1 and c_2 be the complexities of the subgrids. There can be multiple ways to perform the division, and let m be the minimum value of \max(c_1, c_2) in those divisions. The complexity of the grid is m+1.

You are given a grid with H horizontal rows and W vertical columns where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

Find the complexity of the given grid.

Constraints

1 \leq H,W \leq 185

A_{ij} is # or ..

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the complexity of the given grid.

Sample Input 1

3 3
...
.##
.##

Sample Output 1

2

Let us divide the grid by the boundary line between the first and second columns.
The subgrid consisting of the first column has the complexity of 0, and the subgrid consisting of the second and third columns has the complexity of 1, so the whole grid has the complexity of at most 2.

Sample Input 2

6 7
.####.#
#....#.
#....#.
#....#.
.####.#
#....##

Sample Output 2

4

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::cmp;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn main() {
    let hw = read_vec::<usize>();
    let h = hw[0];
    let w = hw[1];
    let mut masu: Vec<Vec<bool>> = Vec::with_capacity(h);
    for _i in 0..h {
        let row1 = read::<String>().chars().collect::<Vec<char>>();
        let mut row2 = vec![false; w];
        for j in 0..w {
            if row1[j] == '#' {
                row2[j] = true;
            }
        }
        masu.push(row2);
    }
    let c = calc(h, w, masu);
    println!("{}", c);
}

/**
 * dp1[r1][r2][c1][f]: 左上が(r1, c1),  右下が(r2, c2)の長方形で複雑度がf以下になる最大のc2
 * dp2[c1][c2][r1][f]: 左上が(r1, c1),  右下が(r2, c2)の長方形で複雑度がf以下になる最大のr2
 */
fn calc(h: usize, w: usize, masu: Vec<Vec<bool>>) -> i32 {
    let max_f = get_max_f(h, w) + 1; // exclusive
    let mut dp1 = get_4d_vec(h, h, w, max_f);
    let mut dp2 = get_4d_vec(w, w, h, max_f);

    // f = 0
    for r1 in 0..h {
        for r2 in r1..h {
            for c1 in 0..w {
                let mut c2 = c1 as i32;
                if r2 == r1 {
                    if c1 < w - 1 {
                        let v = masu[r1][c1];
                        if c1 > 0 && v == masu[r1][c1 - 1] {
                            c2 = dp1[r1][r2][c1 - 1][0];
                        } else {
                            while c2 < (w - 1) as i32 && masu[r1][(c2 + 1) as usize] == v {
                                c2 += 1;
                            }
                        }
                    }
                } else {
                    let c2_prev = dp1[r1][r2 - 1][c1][0];
                    let v_prev = masu[r2 - 1][c1];
                    if c2_prev < 0 || masu[r2][c1] != v_prev {
                        c2 = -1;
                    } else {
                        let c2_prev = dp1[r1][r2 - 1][c1][0];
                        while c2 + 1 <= c2_prev && masu[r2][(c2 + 1) as usize] == v_prev {
                            c2 += 1;
                        }
                    }
                }
                dp1[r1][r2][c1][0] = c2;
                //println!("dp1[{}][{}][{}][{}] = {}", r1, r2, c1, 0, c2);
            }
        }
    }

    for c1 in 0..w {
        for c2 in c1..w {
            for r1 in 0..h {
                let mut r2 = r1 as i32;
                if c2 == c1 {
                    if r1 < h - 1 {
                        let v = masu[r1][c1];
                        if r1 > 0 && v == masu[r1 - 1][c1] {
                            r2 = dp2[c1][c2][r1 - 1][0];
                        } else {
                            while r2 < (h - 1) as i32 && masu[(r2 + 1) as usize][c1] == v {
                                r2 += 1;
                            }
                        }
                    }
                } else {
                    let r2_prev = dp2[c1][c2 - 1][r1][0];
                    let v_prev = masu[r1][c2 - 1];
                    if r2_prev < 0 || masu[r1][c2] != v_prev {
                        r2 = -1;
                    } else {
                        while r2 + 1 <= r2_prev && masu[(r2 + 1) as usize][c2] == v_prev {
                            r2 += 1;
                        }
                    }
                }
                dp2[c1][c2][r1][0] = r2;
                //println!("dp2[{}][{}][{}][{}] = {}", c1, c2, r1, 0, r2);
            }
        }
    }

    // DP
    for f in 1..max_f {
        for r1 in 0..h {
            for r2 in r1..h {
                for c1 in 0..w {
                    // Tate
                    let c2_tate = tate_wari(w, &dp1, r1, r2, c1, f);

                    // Yoko
                    let mut c2_yoko = c2_tate;
                    if c2_yoko < 0 {
                        let r2_c1 = yoko_wari(h, &dp2, c1, c1, r1, f);
                        if r2_c1 >= r2 as i32 {
                            c2_yoko = c1 as i32;
                        }
                    }

                    if c2_yoko >= 0 {
                        while ((c2_yoko + 1) as usize) < w {
                            let r2_next = yoko_wari(h, &dp2, c1, (c2_yoko + 1) as usize, r1, f);
                            if r2_next >= r2 as i32 {
                                c2_yoko += 1;
                                continue;
                            }
                            break;
                        }
                    }

                    dp1[r1][r2][c1][f] = cmp::max(c2_tate, c2_yoko);
                    //println!("dp1[{}][{}][{}][{}] = {}",
                    //    r1, r2, c1, f, dp1[r1][r2][c1][f]);
                }
            }
        }

        for c1 in 0..w {
            for c2 in c1..w {
                for r1 in 0..h {
                    // Yoko
                    let r2_yoko = yoko_wari(h, &dp2, c1, c2, r1, f);

                    // Tate
                    let mut r2_tate = r2_yoko;
                    if r2_tate < 0 {
                        let c2_r1 = tate_wari(w, &dp1, r1, r1, c1, f);
                        if c2_r1 >= c2 as i32 {
                            r2_tate = r1 as i32;
                        }
                    }
                    if r2_tate >= 0 {
                        while ((r2_tate + 1) as usize) < h {
                            let c2_next = tate_wari(w, &dp1, r1, (r2_tate + 1) as usize, c1, f);
                            if c2_next >= c2 as i32 {
                                r2_tate += 1;
                                continue;
                            }
                            break;
                        }
                    }

                    dp2[c1][c2][r1][f] = cmp::max(r2_yoko, r2_tate);
                    //println!(
                    //    "dp2[{}][{}][{}][{}] = {}",
                    //    c1, c2, r1, f, dp2[c1][c2][r1][f]
                    //);
                }
            }
        }
    }

    for f in 0..max_f {
        if dp1[0][h - 1][0][f] == (w - 1) as i32 {
            return f as i32;
        }
    }
    // Never comes here.
    return -1;
}

fn get_4d_vec(s1: usize, s2: usize, s3: usize, s4: usize) -> Vec<Vec<Vec<Vec<i32>>>> {
    let mut v1: Vec<Vec<Vec<Vec<i32>>>> = Vec::with_capacity(s1);
    for _i in 0..s1 {
        let mut v2: Vec<Vec<Vec<i32>>> = Vec::with_capacity(s2);
        for _j in 0..s2 {
            let mut v3: Vec<Vec<i32>> = Vec::with_capacity(s3);
            for _k in 0..s3 {
                let v4 = vec![-1; s4];
                v3.push(v4);
            }
            v2.push(v3);
        }
        v1.push(v2);
    }
    return v1;
}

fn tate_wari(
    w: usize,
    dp1: &[Vec<Vec<Vec<i32>>>],
    r1: usize,
    r2: usize,
    c1: usize,
    f: usize,
) -> i32 {
    let c_x = dp1[r1][r2][c1][f - 1];
    if c_x < 0 {
        -1
    } else if c_x >= (w - 1) as i32 {
        (w - 1) as i32
    } else {
        dp1[r1][r2][(c_x + 1) as usize][f - 1]
    }
}

fn yoko_wari(
    h: usize,
    dp2: &[Vec<Vec<Vec<i32>>>],
    c1: usize,
    c2: usize,
    r1: usize,
    f: usize,
) -> i32 {
    let r_x = dp2[c1][c2][r1][f - 1];
    if r_x < 0 {
        -1
    } else if r_x >= (h - 1) as i32 {
        (h - 1) as i32
    } else {
        dp2[c1][c2][(r_x + 1) as usize][f - 1]
    }
}

fn get_max_f(h: usize, w: usize) -> usize {
    let x = (h as f64).log2().ceil() + (w as f64).log2().ceil();
    return x as usize;
}