#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define rep(i, a, b) for(int i=(a); i<(b); i++)
#define repi(i, a, b) for(int i=(a); i>(b); i--)
#define db(x) (cerr << #x << ": " << (x) << '\n')
#define sync ios_base::sync_with_stdio(false), cin.tie(NULL)
#define cps CLOCKS_PER_SEC
#define tests(t) int t; cin >> t; while(t--)
#define iceil(n, x) (((n) + (x) - 1) / (x))
#define ll long long
#define gcd __gcd
#define eb emplace_back
#define pb push_back
#define pf push_front
#define pob pop_back
#define pof pop_front
#define sz size()
#define all(v) (v).begin(), (v).end()
#define uni(v) sort(all(v)), (v).erase(unique(all(v)), (v).end())
#define pii pair<int, int>
#define vi vector<int>
#define vpii vector<pii>
#define vvi vector<vi>
#define fi first
#define se second
#define mt make_tuple
#define pqueue priority_queue
#define bitcount(x) __builtin_popcount(x)
#define PI acos(-1.0)
#define EPS 1e-9
#define mod 1000000007
using namespace std;

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    cerr << name << " : " << arg1 << '\n';
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}

template<typename T1, typename T2>
ostream& operator << (ostream& os, const pair<T1, T2>& p) { return os << '(' << p.fi << ", " << p.se << ')'; }

template<typename T>
void printv(const T& v) { for(auto i : v) cerr << i << ' '; cerr << '\n'; }

template<typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template<typename T>
using maxpq = priority_queue<T>;

//All indexing is 0-based
using namespace __gnu_pbds;
template<class key, class cmp = std::less<key>>
using ordered_set = tree<key, null_type, cmp, rb_tree_tag, tree_order_statistics_node_update>;
//methods: find_by_order(k); & order_of_key(k);
//To make it an ordered_multiset, use pairs of (value, time_of_insertion)
//to distinguish values which are similar

template<class key, class value, class cmp = std::less<key>>
using ordered_map = tree<key, value, cmp, rb_tree_tag, tree_order_statistics_node_update>;

//Returns no. of values x for which ceil(n / x) == y (y must be > 1).
inline ll CC(ll n, ll y) { return iceil(n, y-1) - iceil(n, y); }

//Returns no. of values x for which floor(n / x) == y
inline ll FF(ll n, ll y) { return n / y - n / (y+1); }

//a and b are assumed to be taken modulo p
inline int add(int a, int b, int p = mod){ int c = a + b; if(c >= p) c -= p; return c; }
inline int sub(int a, int b, int p = mod){ int c = a - b; if(c < 0) c += p; return c; }
inline int mul(int a, int b, int p = mod){ return (a * 1ll * b) % p; }

#define N 1005
#define int ll
// #define trace(...) 42

const int inf = 1e9;

inline bool bit(int n, int b) {
    return (n >> b) & 1;
}

//0-based indexing in ar[]
//1-based indexing in pre[]

int n, m, ar[N][N], pre[N][N];
 
void prep() {
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= m; j++) {
            pre[i][j] = ar[i-1][j-1] + pre[i][j-1] + pre[i-1][j] - pre[i-1][j-1];
        }
    }
}

//0-based query
int query(int a, int b, int c, int d) {
    ++a, ++b, ++c, ++d;
    int ans = pre[c][d] - pre[c][b-1] - pre[a-1][d] + pre[a-1][b-1];
    return ans;
}

int k, mask;
vi v; //horizontal cuts
int dp[N];

int rec(int i) {
    int& ans = dp[i];
    if(ans != -1) return ans;

    ans = inf;
    
    int j = m;

    for(int o = 0; o < v.size()-1; o++) {
        int r1 = v[o], r2 = v[o+1]-1;

        int lo = i-1, hi = m;
        while(hi - lo > 1) {
            int md = (lo + hi) / 2;
            if(query(r1, i, r2, md) > k) hi = md;
            else lo = md;
        }

        // trace(r1, r2, hi);
        j = min(j, hi);
    }

    if(i == j)      ans= inf;
    else if(j == m) ans = 0;
    else            ans = rec(j) + 1;

    // trace(mask, i, j, ans);

    return ans;
}

main()
{   
    #ifdef CP
        freopen("/home/tarun/Desktop/input.txt", "r", stdin);
     // freopen("/home/tarun/Desktop/output.txt", "w", stdout);
    #endif
    sync;
    clock_t clk = clock();
    cerr << "I will return...\n";

    cin >> n >> m >> k;
    rep(i, 0, n) rep(j, 0, m) {
        char c; cin >> c;
        ar[i][j] = c == '1';
    }

    prep();

    int ans = n*m;

    for(mask = 0; mask < (1 << (n-1)); mask++) {
        v.clear();

        v.pb(0);
        rep(i, 0, n-1) {
            if(bit(mask, i)) {
                v.pb(i+1);
            }
        }
        v.pb(n);

        memset(dp, -1, sizeof dp);
        // printv(v);
        ans = min(ans, bitcount(mask) + rec(0));
    }

    cout << ans << '\n';

    cerr << "...don't you ever hang your head.\n";
    cerr << "Time (in ms): " << (double)(clock() - clk) * 1000.0 / cps << '\n';
}

//Compile using:
//g++ -o filename.exe --std=c++11 filename.cpp
//Use -D CP for defining a macro CP in the local environment




Measured memory_bytes: 2560