// May this submission get accepted
#include <bits/stdc++.h>

// エイリアス
using  ll = long signed long;
using ull = long unsigned long;
using  ld = long double;
using namespace std;

// エイリアス (補完・コンパイルが重くなる)
// #include <boost/multiprecision/cpp_int.hpp>
// using mll = boost::multiprecision::cpp_int;

// 汎用マクロ
#define ALL_OF(x) (x).begin(), (x).end()
#define REP(i,n) for (long long i=0, i##_len=(n); i<i##_len; i++)
#define RANGE(i,is,ie) for (long long i=(is), i##_end=(ie); i<=i##_end; i++)
#define DSRNG(i,is,ie) for (long long i=(is), i##_end=(ie); i>=i##_end; i--)
#define STEP(i, is, ie, step) for (long long i=(is), i##_end=(ie), i##_step = (step); i<=i##_end; i+=i##_step)
#define UNIQUE(v) do { sort((v).begin(), (v).end()); (v).erase(unique((v).begin(), (v).end()), (v).end()); } while (false)
#define FOREACH(i,q) for (auto &i : q)
template<class T> bool chmax(T &a, const T b) { if (a < b) {a = b; return true;} return false; }
template<class T> bool chmin(T &a, const T b) { if (a > b) {a = b; return true;} return false; }
constexpr int INF = numeric_limits<int>::max();
constexpr long long LINF = numeric_limits<long long>::max();
constexpr long double EPS = 1e-10L;
#define Yes(q) ((q) ? "Yes" : "No")
#define YES(q) ((q) ? "YES" : "NO")
#define Possible(q) ((q) ? "Possible" : "Impossible")
#define POSSIBLE(q) ((q) ? "POSSIBLE" : "IMPOSSIBLE")
#define IIF(q,t,f) ((q) ? (t) : (f))
#define DUMP(q) DUMP_FUNC(q, #q, __FILE__, __LINE__)
template <typename T> void DUMP_PROC(T x) { if (is_integral<T>() || is_floating_point<T>()) cerr << "\e[32m" << x << "\e[m"; else cerr << x; }
template<> void DUMP_PROC<char>(char x) { cerr << "\e[36m\'" << x << "\'\e[m"; }
template<> void DUMP_PROC<string>(string x) { cerr << "\e[33m\"" << x << "\"\e[m"; }
template <typename T, typename U> void DUMP_PROC(pair<T, U> x) { cerr << "{"; DUMP_PROC(x.first); cerr << ", "; DUMP_PROC(x.second); cerr << "}"; }
template <typename ...T, typename U, U... Seq> void DUMP_PROC(tuple<T...> &x, integer_sequence<U, Seq...>) { (void)(int[]){(cerr << ((const char*[]){"", ", "})[!!Seq] << (DUMP_PROC(get<Seq>(x)), ""), 0)...}; }
template <typename ...T> void DUMP_PROC(tuple<T...> x) {cerr << "{"; DUMP_PROC(x, index_sequence_for<T...>()); cerr << "}";}
template <typename T> void DUMP_PROC(vector<T> x) { cerr << "["; for (auto &xi : x) { DUMP_PROC(xi); cerr << (&xi != &*x.rbegin()?", ":""); } cerr << "]"; }
template <typename T> void DUMP_FUNC(T x, const char* name, const char* fn, int ln) { cerr << "\e[32m[DEBUG]\e[m " << name << ": "; DUMP_PROC(x); cerr << " @ " << fn << "(" << ln << ")" << endl; }
template <class T> T gcd(T a, T b) { if (a < b) swap(a, b); while (b) swap(a %= b, b); return a; }
template <class T> T lcm(const T a, const T b) { return a / gcd(a, b) * b; }

// gcc拡張マクロ
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll

// 標準入出力
struct qin { // query input
    size_t sz;
    qin(size_t _sz = 1) : sz(_sz) {}
    template <typename T> operator T () const { T a; cin >> a; return a; }
    template <typename T> operator vector<T> () const { vector<T> a(sz); for (size_t i = 0; i < sz; i++) cin >> a[i]; return a; }
    template <typename T, typename U> operator pair<T, U> () const { T f; U s; cin >> f >> s; return pair<T, U>(f, s); }
};
qin in1; // input one
template <typename T> void say(const T x, const char* end = "\n") { cout << x << end; }
void say(const ld x, const char* end = "\n") { cout << setprecision(30) << x << end; }
template <typename T> void say(const vector<T> x, const char* sep = " ", const char* end = "\n") { REP(i, x.size()) { cout << x[i] << (i+1 == i_len ? end : sep); } }
template <typename T> void say(const vector<vector<T>> x, const char* sep = " ", const char* end = "\n") { REP(i, x.size()) { say(x[i], sep, end); } }

// モジュール
// 遅延評価セグ木 T: 値の型, U: 操作の型
template<typename T, typename U, typename JOIN_T, typename APPLY_U, typename JOIN_U, typename MULTIPLY_U, typename HALF_U>
class segtree {
    T IT; // T の単位元
    U IU; // U の単位元
    JOIN_T join_t; // 値同士のjoin; T(T: 左の値, T: 右の値)
    APPLY_U apply_u; // 操作を値に適用する; T(T: 操作前の値, U: 操作)
    JOIN_U join_u; // 操作をjoinする; U(U: 古い操作, U: 新しい操作)
    MULTIPLY_U multiply_u; // 操作をn回やる操作を作る; U(U: 操作, ll: 2冪の正整数)
    HALF_U half_u; // 半分の操作を作る; U(U: multiply_uによって2冪倍された操作)
    ll n; // 元の配列のサイズ
    vector<T>    node;
    vector<U>    lazy;
    vector<char> fall; // vector<bool>は空間が良いが時間が悪いのでvector<char>で代用
    // [l, r) を見ており, k を遅延評価
    inline void eval(ll k, ll l, ll r) {
        if (!fall[k]) return;
        node[k] = apply_u(node[k], lazy[k]);
        if (r-l > 1) { // 子があるなら伝播
            lazy[k*2+1] = join_u(lazy[k*2+1], half_u(lazy[k]));
            lazy[k*2+2] = join_u(lazy[k*2+2], half_u(lazy[k]));
            fall[k*2+1] = fall[k*2+2] = true;
        }
        lazy[k] = IU;
        fall[k] = false;
    }
public:
    // コンストラクタ
    segtree(const vector<T> &v, T _it, U _iu, JOIN_T _jot, APPLY_U _apu, JOIN_U _jou, MULTIPLY_U _muu, HALF_U _hau):
        IT(_it), IU(_iu), join_t(_jot), apply_u(_apu), join_u(_jou), multiply_u(_muu), half_u(_hau)
    {
        ll sz = (ll)v.size();
        n = 1; while (n < sz) n *= 2;
        this->node = vector<T   >(n * 2 - 1, IT);
        this->lazy = vector<U   >(n * 2 - 1, IU);
        this->fall = vector<char>(n * 2 - 1, false);
        for (ll i = 0; i < sz; i++) node[n-1 + i] = v[i];
        for (ll i = n-1; i--; )  node[i] = join_t(node[i*2+1], node[i*2+2]);
    }
    // 区間 [a, b) に x を適用（但し, [l, r)を見て今kをいじっている）
    void apply(ll a, ll b, U x, ll k = 0, ll l = 0, ll r = -1) {
        if (r < 0) r = n; // デフォルト値には定数しか入れられない
        eval(k, l, r);
        if (b <= l || r <= a) return; // セグフォ防止
        if (a <= l && r <= b) {
            lazy[k] = join_u(lazy[k], multiply_u(x, r - l));
            fall[k] = true;
            eval(k, l, r);
        } else {
            apply(a, b, x, k*2+1, l, (l+r)/2);
            apply(a, b, x, k*2+2, (l+r)/2, r);
            node[k] = join_t(node[k*2+1], node[k*2+2]);
        }
    }
    // 区間 [a, b) の操作後の値を求める
    T fetch(ll a, ll b, ll k = 0, ll l = 0, ll r = -1) {
        if (r < 0) r = n; // デフォルト値には定数しか入れられない
        if (b <= l || r <= a) return IT; // セグフォ防止
        eval(k, l, r);
        if (a <= l && r <= b) return node[k];
        T vl = fetch(a, b, k*2+1, l, (l+r)/2);
        T vr = fetch(a, b, k*2+2, (l+r)/2, r);
        return join_t(vl, vr);
    }
    // 点 a == 区間 [a, a+1) に x を適用
    inline void applyp(ll a, U x) { apply(a, a+1, x); }
    // 点 a == 区間 [a,a+1) の操作後の値を求める
    inline T fetchp(ll a) { return fetch(a, a+1); }
};
// C++17以降の環境ではこの関数は不要 (テンプレート引数推論が働くため)
template<typename T, typename U, typename JOIN_T, typename APPLY_U, typename JOIN_U, typename MULTIPLY_U, typename HALF_U>
segtree<T, U, JOIN_T, APPLY_U, JOIN_U, MULTIPLY_U, HALF_U> make_segtree(const vector<T> &v, T _it, U _iu, JOIN_T _jot, APPLY_U _apu, JOIN_U _jou, MULTIPLY_U _muu, HALF_U _hau) {
    return segtree<T, U, JOIN_T, APPLY_U, JOIN_U, MULTIPLY_U, HALF_U>(v, _it, _iu, _jot, _apu, _jou, _muu, _hau);
}
// おまけ
const auto SEGTREE_ASGF = [](ll, ll y) { return y; };
const auto SEGTREE_EYE2 = [](ll x, ll) { return x; };
const auto SEGTREE_EYE = [](ll x) { return x; };
auto make_segtree_rminq(const vector<ll> &v) {
    auto minf = [](ll x, ll y) { return min(x, y); };
    return make_segtree(v, LINF, LINF, minf, SEGTREE_ASGF, SEGTREE_ASGF, SEGTREE_EYE2, SEGTREE_EYE);
}
auto make_segtree_rmaxq(const vector<ll> &v) {
    auto maxf = [](ll x, ll y) { return max(x, y); };
    return make_segtree(v, LINF, LINF, maxf, SEGTREE_ASGF, SEGTREE_ASGF, SEGTREE_EYE2, SEGTREE_EYE);
}

// 処理内容
int main() {
    
    ios::sync_with_stdio(false); // stdioを使うときはコメントアウトすること
    cin.tie(nullptr);            // インタラクティブ問題ではコメントアウトすること
    
    ll h, w, k; cin >> h >> w >> k;
    vector<string> s = qin(h);

    ll ans = INF;

    REP(mask, 1LL << (h-1)) {
        
        vector<ll> cr;
        
        vector<ll> bl(h, 0);
        REP(i, h-1) {
            if (mask >> i & 1) {
                bl[i+1] = bl[i] + 1;
            } else {
                bl[i+1] = bl[i];
            }
        }
        ll b = bl.back()+1;

        vector<vector<ll>> wc(b, vector<ll>(w, 0));
        REP(i, h) REP(j, w) {
            wc[bl[i]][j] += s[i][j] == '1';
        }
        vector<vector<ll>> ws(b, vector<ll>(w+1, 0));
        REP(i, b) REP(j, w) {
            ws[i][j+1] = ws[i][j] + wc[i][j];
        }

        // dp[i] := ホワイトチョコがK以上にならないよう割れ目i(1-indexed)で割ったときの割る回数の最小
        vector<ll> dp(w+1, INF);
        dp[0] = 0;
        auto sgt = make_segtree_rminq(dp);
        RANGE(j, 1, w) {
            ll jmin_ok = j;
            ll jmin_ng = -1;
            while (abs(jmin_ok - jmin_ng) > 1) {
                ll jmin_md = (jmin_ok + jmin_ng) / 2;
                bool okay = true;
                REP(i, b) {
                    if (ws[i][j] - ws[i][jmin_md] > k) {
                        okay = false;
                        break;
                    }
                }
                (okay ? jmin_ok : jmin_ng) = jmin_md;
            }
            if (jmin_ok == j) continue;
            sgt.applyp(j, sgt.fetch(jmin_ok, j) + (j < w));
        }
        ll term = sgt.fetchp(w) + b-1;
        chmin(ans, term);
        // cerr << "[DEBUG] " << bitset<10>(mask) << endl;
        // DUMP(term);
    }
    say(ans);
    
}

Measured memory_bytes: 536