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)

#include<iostream>
#include<fstream>
#include<bitset>
#include<string>
#include<vector>
#include<list>
#include<algorithm>
#include<cmath>
#include<map>
#include<set>
#include<iomanip>
#include<queue>
#include<stack>
#include<numeric>
#include<utility>
#include<regex>
#include<climits>

void Init() {
	std::cin.tie(0); std::ios::sync_with_stdio(false);
	struct Init_caller { Init_caller() { Init(); } }caller;
}


#define int long long
#define rep(i,n) for(LL (i)=0;(i)<(n);(i)++)
#define all(a) (a).begin(),(a).end()
#define check() cout<<"! ! !"<<endl
#define endl "\n"
#define _y() cout<<"Yes"<<endl
#define _Y() cout<<"YES"<<endl
#define _n() cout<<"No"<<endl
#define _N() cout<<"NO"<<endl

constexpr long long INF = (int)1e15;
constexpr long long MOD = 1000000007;


using namespace std;


using LL = long long;
using st = string;
template<typename T>using vec = vector<T>;
template<typename T>using vvec = vec<vec<T>>;
template<typename T>using vvvec = vec<vvec<T>>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using vc = vector<char>;
using vvc = vector<vc>;
using vs = vector<st>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vvvb = vector<vvb>;
using qi = queue<int>;
using qc = queue<char>;
using qs = queue<st>;
using si = stack<int>;
using sc = stack<char>;
using ss = stack<st>;
using pi = pair<int, int>;
using ppi = pair<pi, int>;
using mii = map<int, int>;
using mpii = map<pi, int>;
using mib = map<int, bool>;
using mci = map<char, int>;
using msb = map<st, bool>;
using vpi = vector<pi>;
using vppi = vector<ppi>;
using spi = stack<pi>;
using qpi = queue<pi>;



//4,2,8,6,1,7,3,9,5 (x:right y:up is positive)
int dx[] = { -1,0,0,1,-1,-1,1,1,0 };
int dy[] = { 0,1,-1,0,1,-1,1,-1,0 };

template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
	rep(i, v.size()) {
		in >> v[i];
	}

	return in;
}

template<typename T, typename U>
istream &operator>>(istream&in, pair<T, U> &p) {

	in >> p.first >> p.second;
	return in;
}

template<typename T>
ostream &operator<<(ostream &out, vector<T> &v) {
	out << "{";
	rep(i, v.size()) {
		out << v[i] << ",";
	}
	out << "}" << endl;

	return out;
}

template<typename T, typename U>
ostream &operator<<(ostream&out, pair<T, U> &p) {

	out << "{" << p.first << "," << p.second << "}" << endl;
	return out;
}

struct mint {
	int x;
	mint(int x = 0) :x((x%MOD + MOD) % MOD) {}

	mint operator-() const { return mint(-x); }
	mint& operator+=(const mint a) {
		if ((x += a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator-=(const mint a) {
		if ((x += MOD - a.x) >= MOD) x -= MOD;
		return *this;
	}
	mint& operator*=(const mint a) {
		(x *= a.x) %= MOD;
		return *this;
	}
	mint operator+(const mint a) const {
		mint res(*this);
		return res += a;
	}
	mint operator-(const mint a) const {
		mint res(*this);
		return res -= a;
	}
	mint operator*(const mint a) const {
		mint res(*this);
		return res *= a;
	}
	mint pow(int t) const {
		if (!t) return 1;
		mint a = pow(t >> 1);
		a *= a;
		if (t & 1) a *= *this;
		return a;
	}

	mint inv() const {
		return pow(MOD - 2);
	}
	mint& operator/=(const mint a) {
		return (*this) *= a.inv();
	}
	mint operator/(const mint a) const {
		mint res(*this);
		return res /= a;
	}

};

void y_n(bool p) {
	p ? _y() : _n();
}

void Y_N(bool p) {
	p ? _Y() : _N();
}

//MAX,maxpos,MIN,minpos
template<typename T>
pair<pair<T, int>, pair<T, int>> vmaxmin(vector<T> v) {
	int n = v.size();
	int MAX = -INF;
	int MIN = INF;
	int maxpos = 0;
	int minpos = 0;
	rep(i, n) {
		if (MAX < v[i]) {
			maxpos = i;
			MAX = v[i];
		}
		if (MIN > v[i]) {
			minpos = i;
			MIN = v[i];
		}
	}
	return { {MAX,maxpos},{MIN,minpos} };
}

template<typename T>
T vsum(vector<T> v) {
	int n = v.size();
	T sum = 0;
	rep(i, n) {
		sum += v[i];
	}
	return sum;
}

int gcd(int a, int b) {
	if (b == 0) {
		swap(a, b);
	}
	int r;
	while ((r = a % b) != 0) {
		a = b;
		b = r;
	}
	return b;
}

int lcm(int a, int b) {
	return (a / gcd(a, b) * b);
}

bool is_square(int n) {
	if ((int)sqrt(n)*(int)sqrt(n) == n) {
		return true;
	}
	else {
		return false;
	}
}


bool is_prime(int n) {
	if (n <= 1) {
		return false;
	}
	else {
		for (int i = 2; i*i <= n; i++) {
			if (n % i == 0) {
				return false;
			}
		}
	}
	return true;
}

void dec_num(int n, vi &v) {
	int a = 2;
	v.push_back(1);
	v.push_back(n);
	while (a*a <= n) {
		if (n%a == 0) {
			v.push_back(a);
			v.push_back(n / a);

		}
		a++;
	}
	sort(all(v));
}


void dec_prime(int n, vi &v) {
	//v.push_back(1);
	int a = 2;
	while (a*a <= n) {
		if (n % a == 0) {
			v.push_back(a);
			n /= a;
		}
		else {
			a++;
		}
	}
	v.push_back(n);
}

//n= ...*pow(p_i,m[p_i])*...
void dec_prime_e(int n, map<int, int> &m) {
	for (int i = 2; i*i <= n; i++) {
		if (n%i == 0) {
			int e = 0;
			while (n%i == 0) {
				e++;
				n /= i;
			}
			m[i] += e;
		}
	}
	if (n != 1) m[n]++;
}


int sieve_prime(int a, int b) {
	if (a > b)swap(a, b);
	vb s(b + 1, true);
	int cnt_a = 0, cnt_b = 0;
	for (int i = 2; i <= b; i++) {
		for (int j = 2; i*j <= b; j++) {
			s[i*j] = false;
		}
	}
	for (int i = 2; i <= b; i++) {
		if (s[i]) {
			//cout << i << " ";
			if (i < a) {
				cnt_a++;
			}
			cnt_b++;
		}
	}
	return cnt_b - cnt_a;
}


int factorial(int n) {
	int a = 1, ret = 1;
	while (a < n) {
		a++;
		ret *= a;
		//ret %= MOD;
	}
	return ret;
}

int bit_count(int n) {
	int k = (int)log2(n) + 1;
	int ret = 0;
	rep(i, k) {
		if (n&(1LL << i))ret++;
	}
	return ret;
}

//a^(a+1)^(a+2)^...^b
int XOR(int a, int b) {
	if (a == 0) {
		switch (b % 4) {
		case 0:	return b;
		case 1:	return 1;
		case 2:	return (b + 1);
		case 3:	return 0;
		}
	}
	int A = XOR(0, a - 1);
	int B = XOR(0, b);
	return (A ^ B);
}


const int COMBMAX = 4000;
int comb[COMBMAX + 5][COMBMAX + 5];

void init_comb() {
	comb[0][0] = 1;
	rep(i, COMBMAX) {
		rep(j, i + 1) {
			comb[i + 1][j] += comb[i][j];
			//comb[i + 1][j] %= MOD;
			comb[i + 1][j + 1] += comb[i][j];
			//comb[i + 1][j + 1] %= MOD;
		}
	}
}

int combination(int n, int k) {
	if (k<0 || k>n)return 0;
	else return comb[n][k];
}


const int COMBMODMAX = 5000000;
int fac[COMBMODMAX + 5], facinv[COMBMODMAX + 5], inv[COMBMODMAX + 5];

void init_comb_mod() {
	fac[0] = fac[1] = 1;
	facinv[0] = facinv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i < COMBMODMAX; i++) {
		fac[i] = fac[i - 1] * i%MOD;
		inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
		facinv[i] = facinv[i - 1] * inv[i] % MOD;
	}
}

//nCk (mod p)
//nHk = n+k-1Ck
int comb_mod(int n, int k) {
	if (n < k)return 0;
	if (n < 0 || k < 0)return 0;
	return fac[n] * (facinv[k] * facinv[n - k] % MOD) % MOD;
}

//x^n (mod p)
int pow_mod(int x, int n, int p) {
	if (n == 0)return 1;
	int res = pow_mod(x*x%p, n / 2, p);
	if (n % 2 == 1)res = res * x % p;
	return res;
}

struct edge {
	int to;
	int cost;
};

using ve = vector<edge>;
using vve = vector<ve>;


/*****************************************************************************/
signed main() {


	int h, w, k;
	cin >> h >> w >> k;
	vs s(h);
	cin >> s;
	vvi acc(h , vi(w , 0));
	rep(i, h) {
		rep(j, w) {
			if (s[i][j] == '1') {
				acc[i][j]++;
			}
		}
	}
	rep(j, w) {
		rep(i, h-1) {
			acc[i + 1][j] += acc[i][j];
		}
	}
	rep(i, h) {
		rep(j, w-1) {
			acc[i][j + 1] += acc[i][j];
		}
	}
	//cout << acc;
	int ans = INF;
	rep(bit, 1 << (h - 1)) {
		int tmp = bit_count(bit);
		vi yoko(w, 0);
		bool ok = true;
		rep(i, h-1) {
			if (bit&(1 << i)) {
				rep(j, w) {
					if (acc[i][j] > k)ok = false;
					yoko[j] += acc[i][j];
				}
			}
		}
		if (!ok)continue;

		vi tate(h, 0);
		rep(j, w-1) {
			if (acc[h-1][j+1] - yoko[j+1] - tate[h-1] > k) {
				tmp++;
				rep(y, h) {
					tate[y] += acc[y][j];
				}
			}
		}
		rep(i, w) {
			if (acc[h - 1][i] - yoko[i] - tate[h - 1] > k)ok = false;
		}
		//cout << tate << yoko << " " << tmp << endl;;

		if(ok)ans = min(ans, tmp);
	}
	cout << ans;

	/*
	int h, w, k;
	cin >> h >> w >> k;
	vs s(h);
	cin >> s;
	vvi acc(h + 1, vi(w + 1, 0));
	rep(i, h) {
		rep(j, w) {
			if (s[i][j] == '1') {
				acc[i + 1][j + 1]++;
			}
		}
	}
	rep(j, w + 1) {
		rep(i, h) {
			acc[i + 1][j] += acc[i][j];
		}
	}
	rep(i, h + 1) {
		rep(j, w) {
			acc[i][j + 1] += acc[i][j];
		}
	}
	//cout << acc;
	int ans = INF;
	rep(bit, 1 << (h - 1)) {
		int tmp = bit_count(bit);
		vi yoko(w + 1, 0);
		bool ok = true;
		rep(i, h) {
			if (bit&(1 << i)) {
				rep(j, w + 1) {
					if (acc[i + 1][j] > k)ok = false;
					yoko[j] += acc[i + 1][j];
				}
			}
		}
		if (!ok)continue;

		vi tate(h + 1, 0);
		rep(j, w) {
			if (acc[h][j + 1] - yoko[j + 1] - tate[h] > k) {
				tmp++;
				rep(y, h + 1) {
					tate[y] += acc[y][j];
				}
			}
		}
		rep(i, w + 1) {
			if (acc[h][i] - yoko[i] - tate[h] > k)ok = false;
		}
		//cout << tate << yoko << " " << tmp << endl;;

		if (ok)ans = min(ans, tmp);
	}
	cout << ans;*/
}