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: Accepted)

#include<bits/stdc++.h>
#include<iostream>
#include<string>
#include<cmath>
#include<cstdio>
#include<cctype>
#include<cstring>
#include<iomanip>
#include<cstdlib>
#include<ctime>
#include<set>
#include<map>
#include<utility>
#include<queue>
#include<vector>
#include<stack>
#include<sstream>
#include<algorithm>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<pii,pii> piiii;
typedef vector<pii> vii;
typedef vector<int> vi;
typedef queue<int> qi;
typedef queue<char> qc;
typedef queue<string> qs;
typedef vector<char> vc;
typedef vector<string> vs;
typedef map<char,int> mpci;
typedef map<int,int> mpii;
typedef map<string,int> mpsi;
typedef set<int> sei;
typedef set<char> sec;
typedef set<string> ses;
typedef stack<ll> si;
typedef stack<char> sc;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
typedef vector<pll> vpll;
typedef vector<pdd> vdd;
typedef unsigned int uint;
typedef long double ld;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vii> vvii;
/*=====================================================================*/
#define pb push_back
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define sz(a) (int)(a.size())
#define len(a) (int)(a.length())
#define all(s) (s).begin(),(s).end()
#define fi first
#define se second
#define be begin
#define en end
#define m_p make_pair
#define repd(i,n) for(int i=n-1;i>=0;i--)
#define forn(i,p,n) for(int i=p;i<=n;i++)
#define ford(i,p,n) for(int i=n;i>=p;i--)
#define foreach(i,c) for(__typeof(c.begin())i=(c.begin());i!=(c).end();++i)
#define zero(a) memset(a,0,sizeof(a))
#define number(a,num) memeset(a,num,sizeof(a))
#define INF 1e9

/*=====================================================================*/

inline void read(int &x)
{
	short negative=1;
    x=0;
    char c=getchar();
    while(c<'0' || c>'9')
    {
		if(c=='-')
			negative=-1;
		c=getchar();
	}
    while(c>='0' && c<='9')
        x=(x<<3)+(x<<1)+(c^48),c=getchar();
    x*=negative;
}
inline void write(long long x) {
  static long long sta[35];
  long long top = 0;
  do {
    sta[top++] = x % 10, x /= 10;
  } while (x);
  while (top) putchar(sta[--top] + 48);
  puts("");
}
void finish(string s)
{
	cout<<s<<endl;
	exit(0);
}
string int_to_string(int n)
{
	string s="";
	while(n)
	{
		int now=n%10;
		s+=now+'0';
		n/=10;
	}
	reverse(s.begin(),s.end());
	return s;
}
int string_to_int(string s)
{
	int n=0;
	rep(i,s.size())
	{
		n*=10;
		n+=s[i]-'0';
	}
	return n;
}
/*======================================================================*/
ll lcm(int a,int b)
{
	return a/__gcd(a,b)*b;
}
bool prime(int n)
{
	if(n==0||n==1)
	  return false;
	for(int i=2;i*i<=n;i++)
	  if(n%i==0)
	    return false;
	return true;
}
const ll power(int n,int k)
{
	ll t=1;
	rep(i,k)
	  t*=n;
	return t;
}
const string turn2(int n)
{
	string s="";
	while(n!=0)
	{
		s+=(char)(n%2+'0');
		n/=2;
	}
	reverse(s.begin(),s.end());
	return s;
}
string turn(int n,int k)
{
	string s="";
	while(n)
	{
		s+=(char)(n%k+'0');
		n/=k;
	}
	reverse(s.begin(),s.end());
	return s;
}
const string turn16(int n)
{
	string s="";
	while(n!=0)
	{
		if(n%16>9)
		  s+=(char)('A'+n%16-10);
		else
		  s+=(char)('0'+n%16);
		n/=16;
	}
	reverse(s.begin(),s.end());
	return s;
}
const ll quickpower(int n,int k)
{
	if(k==1)
	  return n;
	if(k%2==1)
	  return n*quickpower(n,k/2)*quickpower(n,k/2);
	else
	  return quickpower(n,k/2)*(quickpower(n,k/2));
}
/*
void merge(int a[],int left,int mid,int right)
{
	int n1=mid-left;
	int n2=right-mid;
	for(int i=0;i<n1;i++)
	{
	  l[i]=a[i+left];
    }
	for(int i=0;i<n2;i++)
	{
	  r[i]=a[mid+i];
	}
	r[n2]=l[n1]=INF;
	int i=0;
	int j=0;
	for(int k=left;k<right;k++)
	{
		if(l[i]<=r[j])
		{
			a[k]=l[i++];
		}
		else
		{
			a[k]=r[j++];
		}
	}
}
void mergesort(int a[],int left,int right)
{
	if(left+1<right)
	{
		int mid=(left+right)/2;
		mergesort(a,left,mid);
		mergesort(a,mid,right);
		merge(a,left,mid,right);
	}
}
int binsearch(int x,int v[],int n)
{
	int low=0,high=n-1;
	int mid;
	while(low<=high)
	{
		mid=(low+high)/2;
		if(x<v[mid])
		  high=mid-1;
		else
		  if(x>v[mid])
		    low=mid+1;
		  else
		    return mid+1;
	}
	return -1;
}
int partition(int a[],int left,int right)
{
	int p=a[left];
	int i=left;
	int j=right+1;
	for(;;)
	{
		while(a[++i]<p)
		  if(i>=right)
		    break;
		while(a[j--]>p)
		  if(j<=left)
		    break;
		if(i>=j)
		  break;
		else
		  swap(a[i],a[j]);
	}
	if(j>=left)
	  return j;
	swap(a[left],a[j]);
	return j;
}
void quicksort(int a[],int left,int right)
{
	int q;
	while(right>left)
	{
		q=partition(a,left,right);
	    if(n-q+1==k)
	    {
	        cout<<a[q];
	  		exit(0);
		}
		quicksort(a,left,q-1);
		quicksort(a,q+1,right);
	}
}
void dfs(int n)
{
	if(use[n])
	  return;
	use[n]=true;
	cout<<n<<endl;
	for(int i=0;i<v[n].size();i++)
	  dfs(v[n][i]);
}*/
/*======================================================================*/
const int dx[]={-1,0,1,0};
const int dy[]={0,-1,0,1};
const int month[2][12]={{31,28,31,30,31,30,31,31,30,31,30,31},{31,29,31,30,31,30,31,31,30,31,30,31}};
string s[20];
int h[20],l[1010];
int n,m,cnt=0,k;  
int dp[20][1010];
/*======================================================================*/
int main()
{
  /*
	freopen("input.txt","r",stdin);
	freopen("output.txt","w",stdout);
  */
  /*====================================================================*/
  cin>>n>>m>>k;
  rep(i,n)
  {
  	cin>>s[i];
  }
  memset(dp,0,sizeof(dp));
  forn(i,1,n)
  {
    forn(j,1,m)
    {
    	dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1]+(s[i-1][j-1]=='1');
    }
  }
  vi v;
  int ans=1e9;
  for(int mask=0;mask<(1<<(n-1));mask++)
  {
	  int now=0;
  	v.clear();
  	rep(i,n-1)
  	{
  	  if(mask&(1<<i))	
  	  {
  	  	//cout<<i<<endl;
  	  	now++;
  	  	v.pb(i);
	  }
	}
	v.pb(n-1);
	bool flag=0;
	rep(i,m)
	{
		int la=-1;
		rep(j,v.size())
		{
			if((dp[v[j]+1][i+1]-dp[la+1][i+1]-dp[v[j]+1][i]+dp[la+1][i])>k)
			{				flag=1;
				}
			la=v[j];}
				}
	if(flag)continue;
//	rep(i,v.size())cout<<v[i]<<" ";
//	cout<<endl;
	//cout<<endl;
	int last=-1,lasth=-1;
	rep(i,m+1)
	{
		last=-1;
		rep(j,v.size())
		{
			//cout<<v[j]<<endl;
			//cout<<dp[v[j]+1][m]<<" "<<dp[last][m]<<" "<<dp[v[j]+1][lasth]<<" "<<dp[last][lasth]<<endl;
			//cout<<(dp[v[j]+1][m]-dp[last+1][m])-(dp[v[j]+1][lasth+1]-dp[last+1][lasth+1])<<endl;
			if((dp[v[j]+1][i+1]-dp[last+1][i+1])-(dp[v[j]+1][lasth+1]-dp[last+1][lasth+1])>k)
			{
				lasth=i-1;
				now++;
				break;
			}
			last=v[j];
		}
		//cout<<endl;
	}
	ans=min(ans,now);
  }
  cout<<ans<<endl;
  //cout<<l<<endl;
  return 0;
}