/* #region Head */

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \
    for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \
    for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \
    sort(ALL(c));                                                              \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

// vector 入力
template <typename T> istream &operator>>(istream &is, vc<T> &vec) {
    for (T &x : vec) is >> x;
    return is;
}

// vector 出力 (for dump)
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) {
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}

// vector 出力 (inline)
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) {
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

// pair 入力
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) {
    is >> pair_var.first >> pair_var.second;
    return is;
}

// pair 出力
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map 出力
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        itr++;
        if (itr != map_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}

// um 出力
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        itrcp++;
        if (itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}

// set 出力
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
    os << "{";
    REPI(itr, set_var) {
        os << *itr;
        itr++;
        if (itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                            \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]"        \
            << endl                                                            \
            << "    ",                                                         \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";

/* #endregion */

// Problem
void solve() {
    // code here
    ll h, w, k;
    cin >> h >> w >> k;
    vc<string> s(h);
    cin >> s;
    char black = '0', white = '1';

    // h 方向で全探索，区切り方は 2^(h-1) 通りなので，[0, 1<<(h-1)) を調べる
    ll ret = INF;
    REP(i, 0, 1 << (h - 1)) {
        vvll idxlistlist;
        idxlistlist.push_back({0});
        REP(y, 0, h - 1) {
            ll separate = ((i >> y) & 1);
            if (separate)
                idxlistlist.push_back({y + 1});
            else
                idxlistlist.back().push_back(y + 1);
        }

        bool able = true;

        ll divcnt = 0;             // 横方向の区切り数
        ll sz = SIZE(idxlistlist); // 縦方向の区切り数+1
        vll sizes(sz);
        vvll cnts(2, vll(sz, 0));
        REP(ii, 0, sz) sizes[ii] = SIZE(idxlistlist[ii]);
        // dump(idxlistlist, sizes, cnts);
        bool prev_separated = true; // 直前のループで区切ったか
        REP(x, 0, w) {
            REP(ii, 0, sz) {
                cnts[x % 2][ii] = cnts[(x + 1) % 2][ii]; // 初期化
                REP(jj, 0, sizes[ii]) {
                    // dump(ii, s[idxlistlist[ii][jj]],
                    // s[idxlistlist[ii][jj]][x] == white, cnts[x % 2][ii]);
                    if (s[idxlistlist[ii][jj]][x] == white) cnts[x % 2][ii]++;
                }
            }
            // dump(idxlistlist, sizes, cnts[x % 2]);
            bool ok = true;
            REP(ii, 0, sz) {
                if (cnts[x % 2][ii] > k) {
                    ok = false;
                    break;
                }
            }
            // dump(x, divcnt, prev_separated, cnts[(x + 1) % 2], cnts[x % 2]);
            if (!ok) {
                divcnt++;
                REP(ii, 0, sz) {
                    // if (!prev_separated)
                    cnts[x % 2][ii] -= cnts[(x + 1) % 2][ii];
                    if (cnts[x % 2][ii] > k) {
                        // dump(prev_separated, cnts[(x + 1) % 2], cnts[x % 2]);
                        able = false;
                        break;
                    }
                }
                prev_separated = true;
            } else {
                // dump(cnts[(x + 1) % 2], cnts[x % 2]);
                prev_separated = false;
            }
            if (!able) break;
        }
        // dump(idxlistlist, cnts[(w - 1) % 2], divcnt);
        // dump(idxlistlist, able);
        if (!able) continue;
        chmin(ret, sz - 1 + divcnt);
    }
    cout << ret << endl;
}

// entry point
int main() {
    solve();
    return 0;
}


Measured memory_bytes: 256