Problem:
Score : 500 points

Problem Statement

We have a chocolate bar partitioned into H horizontal rows and W vertical columns of squares.

The square (i, j) at the i-th row from the top and the j-th column from the left is dark if S_{i,j} is 0, and white if S_{i,j} is 1.

We will cut the bar some number of times to divide it into some number of blocks. In each cut, we cut the whole bar by a line running along some boundaries of squares from end to end of the bar.

How many times do we need to cut the bar so that every block after the cuts has K or less white squares?

Constraints

1 \leq H \leq 10

1 \leq W \leq 1000

1 \leq K \leq H \times W

S_{i,j} is 0 or 1.

Input

Input is given from Standard Input in the following format:

H W K
S_{1,1}S_{1,2}...S_{1,W}
:
S_{H,1}S_{H,2}...S_{H,W}

Output

Print the number of minimum times the bar needs to be cut so that every block after the cuts has K or less white squares.

Sample Input 1

3 5 4
11100
10001
00111

Sample Output 1

2

For example, cutting between the 1-st and 2-nd rows and between the 3-rd and 4-th columns - as shown in the figure to the left - works.

Note that we cannot cut the bar in the ways shown in the two figures to the right.

Sample Input 2

3 5 8
11100
10001
00111

Sample Output 2

0

No cut is needed.

Sample Input 3

4 10 4
1110010010
1000101110
0011101001
1101000111

Sample Output 3

3

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#ifdef LOCAL
#include <header.hpp>
#else
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#endif
#define lp(i, l, r) for (int i = int(l); i <= int(r); ++i)
#define rp(i, r, l) for (int i = int(r); i >= int(l); --i)
#define ls(i, s) for (int i = 0; s[i]; ++i)
#define rs(i, s) for (int i = strlen(s) - 1; i >= 0; --i)
#define lv(i, a) for (int i = 0; i < int(a.size()); ++i)
#define rv(i, a) for (int i = int(a.size()) - 1; i >= 0; --i)
#define fast ios::sync_with_stdio(0), cin.tie(0)
#define prec(a) cout << setprecision(a) << fixed
#define freo freopen
#define many for (int T = -1; T < 0 && cin >> T, T--;)
#define appl(x, f, a)                                                          \
    for (auto &x : a)                                                          \
    f
#define rang(a) begin(a), end(a)
#define gene template <class T>
#define elif else if
#define intm modular_arithmetic::integer
#define bcnt __builtin_popcount
#ifndef LOCAL
#define endl '\n'
#define assert
#endif
using namespace std;
using namespace __gnu_pbds;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
gene T rint(T l, T r) { return uniform_int_distribution<T>(l, r)(rng); }
template <class A, class B> B conv(const A &a, B b = B()) {
    stringstream s;
    s << a, s >> b;
    return b;
}
vector<string> spli(const string &s) {
    vector<string> r;
    for (int i = 0, j; i < int(s.size()); ++i)
        if (s[i] != ' ') {
            r.push_back("");
            for (j = i; j < int(s.size()) && s[j] != ' '; ++j)
                r.back().push_back(s[j]);
            i = j - 1;
        }
    return r;
}
template <class T = int> T inf() { return numeric_limits<T>::max(); }
gene T floor(const T &a, const T &b) {
    assert(b != 0);
    return (a > 0 && b > 0) || (a < 0 && b < 0)
               ? abs(a) / abs(b)
               : -(abs(a) + abs(b) - 1) / abs(b);
}
gene T ceil(const T &a, const T &b) {
    assert(b != 0);
    return (a > 0 && b > 0) || (a < 0 && b < 0) ? (abs(a) + abs(b) - 1) / abs(b)
                                                : -abs(a) / abs(b);
}
gene bool tmin(T &a, T b) { return b < a ? a = b, true : false; }
gene bool tmax(T &a, T b) { return b > a ? a = b, true : false; }
gene auto min(const T &a) { return *min_element(rang(a)); }
gene auto max(const T &a) { return *max_element(rang(a)); }
gene auto sum(const T &a) {
    return accumulate(rang(a), (typename T::value_type)0);
}
template <> auto sum(const vector<int> &a) { return accumulate(rang(a), 0ll); }
template <class T, int N, class I>
auto gath(const T (&a)[N], const vector<I> &b) {
    vector<T> r;
    for (auto i : b)
        r.push_back(a[i]);
    return r;
}
template <class T, class I> auto gath(const T &a, const vector<I> &b) {
    vector<typename T::value_type> r;
    for (auto i : b)
        r.push_back(a[i]);
    return r;
}
template <class T, class C = less<typename T::value_type>>
void sort(T &a, C c = C()) {
    sort(rang(a), c);
}
gene void reve(T &a) { reverse(rang(a)); }
gene void uniq(T &a) { sort(a), a.erase(unique(rang(a)), end(a)); }
gene void shuf(T &a) { shuffle(rang(a), rng); }
gene void merg(T l, T m, T r) { inplace_merge(l, m, r); }
gene void in(T &a) { cin >> a; }
template <class A, class... B> void in(A &a, B &... b) { cin >> a, in(b...); }
void ou() { cout << endl; }
gene void ou(const T &a) { cout << a << endl; }
template <class A, class... B> void ou(const A &a, const B &... b) {
    cout << a << ' ', ou(b...);
}
template <class F, class S> istream &operator>>(istream &s, pair<F, S> &a) {
    return s >> a.first >> a.second;
}
template <class F, class S>
ostream &operator<<(ostream &s, const pair<F, S> &a) {
    return s << '(' << a.first << ", " << a.second << ')';
}
gene istream &operator>>(istream &s, vector<T> &a) {
    for (int i = -1; i < 0 && (!a.size() && (cin >> i, a.resize(i), 0), i = 0),
             i < int(a.size());)
        s >> a[i++];
    return s;
}
gene ostream &operator<<(ostream &s, const vector<T> &a) {
    lv(i, a) cout << a[i] << (i + 1 == int(a.size()) ? "" : " ");
    return s;
}
gene using bbst =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
gene using heap = __gnu_pbds::priority_queue<T, greater<T>, pairing_heap_tag>;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef string str;
// The templates end here.
int main() {
    fast, prec(12);
    int h, w, k;
    in(h, w, k);
    vector<str> a(h);
    in(a);
    int ans = inf();
    lp(mask, 0, (1 << (h - 1)) - 1) {
        int this_ans = bcnt(mask);
        vi sm(bcnt(mask) + 1);
        lp(i, 0, w - 1) {
            vi c(1, 0);
            lp(j, 0, h - 1) {
                c.back() += (a[j][i] - '0');
                if ((mask >> j) & 1) {
                    c.push_back(0);
                }
            }
            assert(c.size() == sm.size());
            int fail = 0;
            lv(j, c) {
                if (sm[j] + c[j] > k) {
                    fail = 1;
                }
            }
            if (fail) {
                ++this_ans;
                sm = c;
            } else {
                lv(j, c) sm[j] += c[j];
            }
        }
        tmin(ans, this_ans);
    }
    ou(ans);
    return 0;
}