use std::cmp;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let h: usize = sc.read();
    let w: usize = sc.read();
    let k: usize = sc.read();
    let board: Vec<Vec<usize>> = (0..h)
        .map(|_| {
            sc.read::<String>()
                .chars()
                .map(|c| c as usize - '0' as usize)
                .collect()
        })
        .collect();
    let sum = CumulativeSum::new(&board, 0);
    let mut ans = 1 << 30;
    for mask in 0..(1 << (h - 1)) {
        if let Some(sum) = calc(mask, &sum, (h, w), k) {
            ans = cmp::min(ans, sum);
        }
    }

    println!("{}", ans);
}

fn calc(mask: usize, sum: &CumulativeSum<usize>, (h, w): (usize, usize), k: usize) -> Option<u32> {
    let mut line = vec![];
    for i in 0..(h - 1) {
        if mask & (1 << i) != 0 {
            line.push(i);
        }
    }
    let mut prev = 0;
    let mut vertical = vec![];
    for &l in line.iter() {
        vertical.push((prev, l));
        prev = l + 1;
    }
    vertical.push((prev, h - 1));

    let mut ans = 0;
    let mut prev = 0;
    for j2 in 0..w {
        let mut ok = true;
        for &(i1, i2) in vertical.iter() {
            let sum = sum.get_sum(i1, prev, i2, j2);
            if sum > k {
                ok = false;
            }
        }

        if !ok {
            if prev < j2 {
                prev = j2;
                ans += 1;
            } else {
                return None;
            }
        }
    }

    Some(ans + mask.count_ones())
}

pub struct CumulativeSum<T> {
    ny: usize,
    nx: usize,
    sum: Vec<Vec<T>>,
}

impl<T> CumulativeSum<T>
where
    T: Copy + std::ops::Add<Output = T> + std::ops::Sub<Output = T>,
{
    pub fn new(a: &Vec<Vec<T>>, init: T) -> CumulativeSum<T> {
        assert!(a.len() > 0);
        let ny = a.len();
        let nx = a[0].len();
        let mut sum = vec![vec![init; nx + 1]; ny + 1];
        for i in 0..ny {
            for j in 0..nx {
                sum[i + 1][j + 1] = a[i][j] + sum[i][j + 1] + sum[i + 1][j] - sum[i][j];
            }
        }
        CumulativeSum {
            ny: ny,
            nx: nx,
            sum: sum,
        }
    }

    pub fn get_sum(&self, y1: usize, x1: usize, y2: usize, x2: usize) -> T {
        assert!(y1 <= y2 && x1 <= x2);
        assert!(y2 <= self.ny - 1);
        assert!(x2 <= self.nx - 1);
        return self.sum[y2 + 1][x2 + 1] + self.sum[y1][x1]
            - self.sum[y1][x2 + 1]
            - self.sum[y2 + 1][x1];
    }
}
pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}


Measured memory_bytes: 4352