#include <bits/stdc++.h>
using namespace std;
/*{{{*/  //template
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
constexpr int INF = numeric_limits<int>::max()/2;
constexpr long long LINF = numeric_limits<long long>::max()/3;
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr<<#x<<":"<<x<<endl
#define debug2(x,y) cerr<<#x<<","<<#y":"<<x<<","<<y<<endl
//struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double{ double d; explicit Double(double x) : d(x){} };
ostream& operator<<(ostream& os,const Double x){ os << fixed << setprecision(20) << x.d; return os; }
template<typename T> ostream& operator<<(ostream& os,const vector<T>& vec){ os << "["; for(const auto& v : vec){ os << v << ","; } os << "]"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os, const map<T,U>& mp){ os << "{"; for(auto& p : mp){ os << p << ","; } os << "}"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os,const pair<T,U>& p){ os << "(" << p.first << ","<< p.second <<")"; return os; }
template<typename T> ostream& operator<<(ostream& os,const set<T>& st){ os<<"{"; for(T v:st) os<<v<<","; os <<"}"; return os; }
template<typename T,typename U> inline void chmax(T &x,U y){ if(y>x) x = y; }
template<typename T,typename U> inline void chmin(T &x,U y){ if(y<x) x = y; }
using ll = long long;
using ull = unsigned long long;
using pii = std::pair<int,int>;
using vi = std::vector<int>;
typedef vector<vi> vvi;
ll gcd(ll a,ll b){ if(b==0) return a; else return gcd(b,a%b); }
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
//constexpr double eps = 1e-14; 
constexpr double eps = 1e-10; 
constexpr ll mod = 1e9+7;
const int dx[]={1,0,-1,0} ,dy[] = {0,1,0,-1};
/*}}}*/

template<typename T=int>
struct Sum2D{
    int H,W;
    vector<vector<T>> tbl;
    Sum2D(int h,int w) : H(h), W(w), tbl(h+10,vector<T>(w+10,0)){}
    void add(int x,int y,T a){
        tbl[x+1][y+1]+=a;
    }
    void run(){
        for(int x=0;x<=H;x++) for(int y=0;y<=W;y++) tbl[x][y+1]+=tbl[x][y];
        for(int x=0;x<=H;x++) for(int y=0;y<=W;y++) tbl[x+1][y]+=tbl[x][y];
    }
    /* [sx,gx) x [sy,gy)の領域の値を取る */
    T get(int sx,int sy,int gx,int gy){
        return tbl[gx][gy]-tbl[sx][gy]-tbl[gx][sy]+tbl[sx][sy];
    }
    /* 左下が(0,0) */
    void print(){
        for(int y=W;y>=0;y--){
            for(int x=0;x<=H;x++){
                cerr << tbl[x][y] << " ";
            }
            cerr << "\n";
        }
    }
};

int main(){
    int h,w,k; cin >> h >> w >> k;
    vector<vector<int>> tbl(h, vector<int>(w));
    rep(i,h){
        string s; cin >> s;
        rep(j,w){
            tbl[i][j] = s[j]-'0';
        }
    }

    Sum2D<int> s(h,w);
    rep(i,h){
        rep(j,w){
            s.add(i,j,tbl[i][j]);
        }
    }
    s.run();

    int ans = INF;
    for(int mask=0;mask<(1<<h);mask++){
        if(!(mask & (1<<(h-1)))) continue;
        //cout << "mask = " << static_cast<bitset<4>>(mask) << endl;
        int cnt = __builtin_popcount(mask)-1;

        bool ng = false;

        int l = 0;
        for(int j=0;j<w;j++){
            int u = 0;
            for(int i=0;i<h;i++){
                if(mask & (1<<i)){
                    int num = s.get(u, l, i+1, j+1);
                    //printf("(%d,%d)->(%d,%d) = %d\n", u,l, i+1, j+1, num);
                    if(num > k){
                        // 縦はjに線を入れる
                        cnt++;
                        l = j;
                        if(s.get(u,l,i+1,j+1) > k){
                            ng = true;
                        }
                        break;
                    }
                    u = i+1;
                }
            }
        }

        if(ng) continue;
        chmin(ans, cnt);
    }
    cout << ans << endl;
}


Measured memory_bytes: 3704