#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

type BoxResult<T> = Result<T, Box<std::error::Error>>;


fn main() {
    let mut scanner = Scanner::new(stdin());
    let (h, w, k) = scanner.read_three::<usize>().unwrap();
    let mut is_white = vec![vec![false; w]; h];
    for i in 0..h {
        let line = scanner.read_chars().unwrap();
        for j in 0..w {
            is_white[i][j] = line[j] == '1';
        }
    }
    let mut cumsum = vec![];
    for i in 0..h {
        cumsum.push(is_white[i].iter().scan(0, |state, &val| {
            if val {
                *state += 1;
            }
            Some(*state)
        }).collect::<Vec<_>>());
    }
    let ans = solve(h, w, &cumsum, k);
    println!("{}", ans);
}

fn solve(h: usize, w: usize, cumsum: &[Vec<usize>], k: usize) -> usize {
    let mut minimum = std::usize::MAX;
    for i in 0..(1 << (h - 1)) {
        let mut div = 0;
        let mut splits = vec![];
        let mut crt = 0;
        for j in 0..(h - 1) {
            if ((i >> j) & 1) == 1 {
                splits.push((crt, j));
                crt = j + 1;
                div += 1;
            }
        }
        splits.push((crt, h - 1));
        if let Some(num) = count(&splits, w, cumsum, k) {
            minimum = min(num + div, minimum);
        }
    }
    minimum
}

fn count(splits: &[(usize, usize)], w: usize, cumsum: &[Vec<usize>], k: usize) -> Option<usize> {
    let mut sum = 0;
    let mut crt = 0;
    if !check(0, 0, splits, cumsum, k) {
        return None;
    }
    for j in 1..w {
        if !check(crt, j, splits, cumsum, k) {
            if !check(j, j, splits, cumsum, k) {
                return None;
            }
            crt = j;
            sum += 1;
        }
    }
    Some(sum)
}

fn check(start: usize, end: usize, splits: &[(usize, usize)], cumsum: &[Vec<usize>], k: usize) -> bool {
    for &(i, j) in splits {
        let mut sum = 0;
        for l in i..(j + 1) {
            sum += if start == 0 { cumsum[l][end] } else { cumsum[l][end] - cumsum[l][start - 1] };
        }
        if sum > k {
            return false;
        }
    }
    true
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    #[allow(dead_code)]
    fn read_two<T>(&mut self) -> BoxResult<(T, T)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let nums = self.read_vector()?;
        Ok((nums[0], nums[1]))
    }
    #[allow(dead_code)]
    fn read_three<T>(&mut self) -> BoxResult<(T, T, T)>
    where
        T: FromStr,
        T: Copy,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let nums = self.read_vector()?;
        Ok((nums[0], nums[1], nums[2]))
    }
    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}


Measured memory_bytes: 4352