#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cctype>
#include <cassert>
#include <climits>
#include <string>
#include <bitset>
#include <cfloat>
#include <unordered_set>
#include <iomanip>
//#pragma GCC optimize("Ofast")  //デバッグ時にoptimized-outされて邪魔だった
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int,int> > vpii;
typedef vector<vector<int> > vvi;
typedef vector<vector<char> > vvc;
typedef vector<vector<string> > vvs;
typedef vector<vector<ll> > vvll;
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define irep(it, stl) for(auto it = stl.begin(); it != stl.end(); it++)
#define drep(i,n) for(int i = (n) - 1; i >= 0; --i)
#define fin(ans) cout << (ans) << '\n'
#define mp(p,q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define floatprec(dig) fixed << setprecision(dig)
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
#define itn int;
#define invar(typ, var) typ var; cin >> var;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template <class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;} return 0;}
template <class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;} return 0;}
struct io{io(){ios::sync_with_stdio(false);cin.tie(0);}};
const int INF = INT_MAX;
const ll LLINF = 1LL<<60;
const ll MOD = 1000000007;
const double EPS = 1e-9;

int dp[12][1002];

bool solve(int H, int W, int K,
    vector<string>& zu, unordered_set<int>& below,
    int& ovalue) {
  //dp
  //initialize
  rep(i, 12) rep(j, 1002) dp[i][j] = 0;
  
  ll kugiri = 0;
  
  rep(j, W) {
    bool isc = false;
    rep(i, H) {
      int ii = i + 1; int jj = j + 1;
      dp[ii][jj] = (zu[i][j] == '1' ? 1 : 0);
      //上に仕切りが無い
      //ii == 2のとき，i=0があると，だめ
      if(below.find(ii-2) == below.end()) {
        //無い => 上から足す
        dp[ii][jj] += dp[ii-1][jj] - dp[ii-1][jj-1];
      }
      
      dp[ii][jj] += dp[ii][jj-1];
      
      if(dp[ii][jj] > K) {
        //オーバーした
        isc = true;
        break;
      }
    }
    
    if(isc) {
      //1列前をクリア
      rep(i, H) dp[i + 1][j + 1 - 1] = 0;
      
      rep(i, H) {
        int ii = i + 1; int jj = j + 1;
        dp[ii][jj] = (zu[i][j] == '1' ? 1 : 0);
        //上に仕切りが無い
        //ii == 2のとき，i=0があると，だめ
        if(below.find(ii-2) == below.end()) {
          //無い => 上から足す
          dp[ii][jj] += dp[ii-1][jj] - dp[ii-1][jj-1];
        }
        
        dp[ii][jj] += dp[ii][jj-1];
        
        if(dp[ii][jj] > K) {
          return false;  //1列前クリアしてもだめ
        }
      }
      
      //区切って成功
      kugiri++;
    }
  }
  
  ovalue = kugiri;
  
  return true;
}

signed main(void) {
  cin.tie(0); ios::sync_with_stdio(false);
  
  invar(int, H);
  invar(int, W);
  invar(int, K);
  
  vector<string> zu(H);
  rep(i, H){
    cin >> zu[i];
  }
  
  ll minv = INF / 2;
  //まず，2^(H-1)通り試してみる
  //縦割り
  for(int bit = 0; bit < (1 << (H-1)); ++bit) {
    //下に仕切りがあるもの
    unordered_set<int> below;
    below.clear();
    int ctt = 0;
    for(int i=0; i<H-1; ++i) {
      if(bit & (1 << i)) {
        below.insert(i);
        ctt ++;
      }
    }
    
    int ovalue = 0;
    if(solve(H, W, K, zu, below, ovalue)) {
      chmin(minv, (ll)ovalue + (ll)below.size());
    }
    
    //cout << below.size() << "," << ctt << endl;
  }
  
  fin(minv);
}


Measured memory_bytes: 384