/**
 *    author:  zjsdut
 *    created: 2020/03/23 11:53:32
 **/
#include <bits/stdc++.h>

using namespace std;

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

template <typename A, typename B> bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template <typename A, typename B> bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

template <typename T> istream &operator>>(istream &stream, vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

void scan() {}

template <class T, class... Args> void scan(T &a, Args &... rest) {
  cin >> a;
  scan(rest...);
}

using ll = long long;
using vl = vector<ll>;
using vb = vector<bool>;
using vi = vector<int>;
using pii = pair<int, int>;
template <typename T> using vv = vector<vector<T>>;
#define rng(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rep(n)                                                                 \
  for (int TOKENPASTE2(_iter_, __LINE__) = 0,                                  \
                               TOKENPASTE2(_num_, __LINE__) = (int)(n);        \
       TOKENPASTE2(_iter_, __LINE__) < TOKENPASTE2(_num_, __LINE__);           \
       ++TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define UB(cont, x) int(upper_bound(all(cont), x) - begin(cont))

template <typename T>
ostream &operator<<(ostream &stream, const vector<T> &vec) {
  if (!vec.empty()) {
    stream << vec[0];
    for (size_t i = 1; i != vec.size(); ++i)
      stream << ' ' << vec[i];
  }
  return stream;
}

template <typename T> void print(const vector<T> &t) { cout << t << '\n'; }

template <typename T> void print(const vector<vector<T>> &t) {
  for (const auto &row : t) {
    print(row);
  }
}

template <typename T> void print(const T &t) { cout << t << ' '; }

template <typename T, typename... Args>
void print(const T &t, const Args &... rest) {
  print(t);
  print(rest...);
}

template <typename T> void println(const T &t) { cout << t << '\n'; }

template <typename T, typename... Args>
void println(const T &t, const Args &... rest) {
  print(t);
  println(rest...);
}
template <typename int_t> inline int_t lowbit(int_t x) { return x & -x; }

inline unsigned h_bit(unsigned long long x) {
  return sizeof(unsigned long long) * 8 - __builtin_clzll(x);
}

unsigned long long pow2(unsigned long long x) { // round up to power of 2
  return x == lowbit(x) ? x : 1ull << h_bit(x);
}
template <typename T> int get_bit(T a, int i) { return a >> i & 1; }

// debug code by tourist
string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#if defined LOCAL && !defined DUIPAI
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
#define popcnt(x) __builtin_popcountll((x))

int a[10][1000];
int main() {
#if defined LOCAL && !defined DUIPAI
  ifstream in("in.txt");
  cin.rdbuf(in.rdbuf());
#endif
  int H, W, K;
  scan(H, W, K);
  rng(i, 0, H) {
    string s;
    scan(s);
    rng(j, 0, W) { a[i][j] = s[j] - '0'; }
  }

  auto check = [&](int s) {
    //    cout <<"s: " << mask << endl;
    s |= 1 << (H - 1);
    int pre = 0;
    vv<int> cnt;
    rng(i, 0, H) {
      if (get_bit(s, i)) {
        vi t;
        rng(j, 0, W) {
          int sum = 0;
          up(row, pre, i) { sum += a[row][j]; }
          if (sum > K) {
            return INT_MAX;
          }
          if (!t.empty()) sum += t.back();
          t.pb(sum);
        }
        cnt.pb(t);
        pre = i + 1;
      }
    }

    //    FOR (r, cnt) {
    //      println(r);
    //    }
    int n = popcnt(s);
    assert(SZ(cnt) == n);
    vi lim(n, K), index(n, 0);
    int ans = 0;
    while (true) {
      rng (i, 0, n) {
        while (index[i] < W && cnt[i][index[i]] <= lim[i]) {
          ++index[i];
        }
      }
      int t = *min_element(all(index));
      assert(t > 0);
      if (t == W) break;
      ++ans;
      rng (i, 0, n) {
        lim[i] = cnt[i][t - 1] + K;
      }
    }
//    debug(n, ans + n - 1);
    return ans + n - 1;
  };
  int ans = INT_MAX;
  int tot = 1 << (H - 1);
  rng(s, 0, tot) { chkmin(ans, check(s)); }
  println(ans);
  return 0;
}


Measured memory_bytes: 384