Ivan is a student at Berland State University (BSU). There are n days in Berland week, and each of these days Ivan might have some classes at the university.

There are m working hours during each Berland day, and each lesson at the university lasts exactly one hour. If at some day Ivan's first lesson is during i-th hour, and last lesson is during j-th hour, then he spends j - i + 1 hours in the university during this day. If there are no lessons during some day, then Ivan stays at home and therefore spends 0 hours in the university.

Ivan doesn't like to spend a lot of time in the university, so he has decided to skip some lessons. He cannot skip more than k lessons during the week. After deciding which lessons he should skip and which he should attend, every day Ivan will enter the university right before the start of the first lesson he does not skip, and leave it after the end of the last lesson he decides to attend. If Ivan skips all lessons during some day, he doesn't go to the university that day at all.

Given n, m, k and Ivan's timetable, can you determine the minimum number of hours he has to spend in the university during one week, if he cannot skip more than k lessons?

Input

The first line contains three integers n, m and k (1 ≤ n, m ≤ 500, 0 ≤ k ≤ 500) — the number of days in the Berland week, the number of working hours during each day, and the number of lessons Ivan can skip, respectively.

Then n lines follow, i-th line containing a binary string of m characters. If j-th character in i-th line is 1, then Ivan has a lesson on i-th day during j-th hour (if it is 0, there is no such lesson).

Output

Print the minimum number of hours Ivan has to spend in the university during the week if he skips not more than k lessons.

Examples

Input

2 5 1
01001
10110


Output

5


Input

2 5 0
01001
10110


Output

8

Note

In the first example Ivan can skip any of two lessons during the first day, so he spends 1 hour during the first day and 4 hours during the second day.

In the second example Ivan can't skip any lessons, so he spends 4 hours every day.

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class codeforces 
{ 
   static class Student{
       long x,y;//z;
        Student(long x,long y){
            this.x=x;
            this.y=y;
            //this.z=z;
        }
    }
    static int prime[];
    static void sieveOfEratosthenes(int n) 
    { 
        // Create a boolean array "prime[0..n]" and initialize 
        // all entries it as true. A value in prime[i] will 
        // finally be false if i is Not a prime, else true. 
        int pos=0;
        prime= new int[n+1]; 
        for(int p = 2; p*p <=n; p++) 
        { 
            // If prime[p] is not changed, then it is a prime 
            if(prime[p] == 0)
            { 
                // Update all multiples of p
                prime[p]=p;
                for(int i = p*p; i <= n; i += p)
                    if(prime[i]==0)
                    prime[i] = p; 
            } 
        } 
    }
/*static    class Sortbyroll implements Comparator<Student> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public long compare(Student c, Student b) 
    {
        return c.x-b.x;
    } 
} */
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
 
    static class Edge{
        int a,b;
        Edge(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
    static class Trie{
        HashMap<Character,Trie>map;
         int c;
        Trie(){
            map=new HashMap<>();
            //z=null;
            //o=null;
            c=0;
        }
    }
    //static long ans;
    static int parent[];
    static int rank[];
    static int b[];
    static int h[];
    static int ho[][];
    static int seg[];
    //static int pos;
    //static long mod=1000000000+7;
    //static int dp[][];
    static HashMap<String,Integer>map;
    static PriorityQueue<Student>q=new PriorityQueue<>();
    //static Stack<Integer>st;
   // static ArrayList<Character>ans;
    static ArrayList<ArrayList<Integer>>adj;
    //static ArrayList<ArrayList<Integer>>tr;
    static ArrayList<HashMap<Long,Student>>map1;
    static ArrayList<HashMap<Long,Long>>map2;
    //static long ans;
    static int pos;
    static Trie root;
    static long fac[];
    static int s,d;
    static int gw,gb;
    static long mod=(long)(998244353);
    static long ans1;
    static long ans2;
    static void solve()throws IOException{
        FastReader sc=new FastReader();
        int n,m,k,i,j,l,c,left;
        n=sc.nextInt();
        m=sc.nextInt();
        k=sc.nextInt();
        String s[]=new String[n];
        for(i=0;i<n;i++)
            s[i]=sc.nextLine();
        int dp[][]=new int[n+1][k+1];
        //HashMap<Integer,Integet>map=new HashMap<>();
        int count[][]=new int[n][m+2];
        int ans[][]=new int[k+1][n+1];
        for(i=0;i<n;i++){
            c=0;
            //f[i]=m+1;
            for(j=0;j<m;j++){
                if(s[i].charAt(j)=='1'){
                    ++c;
                   // f[i]=Math.min(f[i],i);
                }
                if(count[i][c]==0)
                    count[i][c]=j+1;
            }
           count[i][m+1]=c;
        }
        for(i=0;i<n;i++){
            //dp[i+1][0]=count[i][k+1];
            if(count[i][m+1]!=0)
                dp[i+1][0]=count[i][count[i][m+1]]-count[i][1]+1;
            for(j=1;j<=Math.min(count[i][m+1],k);j++){
                dp[i+1][j]=Integer.MAX_VALUE;
               // x=0;
                for(l=1;l<=Math.min(j+1,count[i][count[i][m+1]]);l++){
                    left=j-(l-1);
                    if(count[i][count[i][m+1]-left]>=count[i][l])
                    dp[i+1][j]=Math.min(dp[i+1][j],count[i][count[i][m+1]-left]-count[i][l]+1);
                    else
                        dp[i+1][j]=0;
                }
            }
        }
        for(i=0;i<=k;i++){
            for(j=1;j<=n;j++){
                ans[i][j]=Integer.MAX_VALUE;
                for(l=0;l<=i;l++){
                    ans[i][j]=Math.min(ans[i][j],dp[j][l]+ans[i-l][j-1]);
                }
            }
        }
        System.out.println(ans[k][n]);
    }
    static Student dfs(int p,int c,int a[],int b[]){
        long x1=0,y=0;
        Student s;
        for(Integer x:adj.get(c)){
            if(x==p)
                continue;
            s=dfs(c,x,a,b);
            x1+=s.x;
            y+=s.y;
        }
        long t=y+(long)a[c]-x1+(long)b[c];
        if(t<(long)0||t%(long)2!=0)
            pos=1;
        x1+=t/(long)2;
        y+=(long)a[c]-t/(long)2;
        return new Student(x1,y);
    }

    static void dfs2(int p,int c,long dp1[][],long dp[]){
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs2(c,x,dp1,dp);
            dp[c]=Math.max(dp[c],dp[x]);
            if(dp1[c][0]==Long.MIN_VALUE)
                dp1[c][0]=dp[x];
            else if(dp1[c][0]<=dp[x]){
                dp1[c][1]=dp1[c][0];
                dp1[c][0]=dp[x];
            }
            else
                dp1[c][1]=Math.max(dp1[c][1],dp[x]);
        }
    }
    static void dfs(int p,int c,int a[],long dp[]){
        dp[c]=a[c];
        for(Integer x: adj.get(c)){
            if(x==p)
                continue;
            dfs(c,x,a,dp);
            dp[c]+=dp[x];
        }
    }
    static void dfs(int x,int y,char f[][],int n,int m){
        f[x][y]='u';
        if(x+1<n){
            if(f[x+1][y]=='*')
                ++pos;
            if(f[x+1][y]=='.')
                dfs(x+1,y,f,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='*')
                ++pos;
            if(f[x-1][y]=='.')
                dfs(x-1,y,f,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='*')
                ++pos;
            if(f[x][y+1]=='.')
                dfs(x,y+1,f,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='*')
                ++pos;
            if(f[x][y-1]=='.')
                dfs(x,y-1,f,n,m);
        }
    }
    static void fill(int x,int y,char f[][],int dp[][],int n,int m){
        dp[x][y]=pos;
        f[x][y]='*';
           if(x+1<n){
            if(f[x+1][y]=='u')
                fill(x+1,y,f,dp,n,m);
        }
        if(x-1>=0){
            if(f[x-1][y]=='u')
                fill(x-1,y,f,dp,n,m);
        }
        if(y+1<m){
            if(f[x][y+1]=='u')
                fill(x,y+1,f,dp,n,m);
        }
        if(y-1>=0){
            if(f[x][y-1]=='u')
                fill(x,y-1,f,dp,n,m);
        }
    }
    static boolean check(String s){
        int i=0,j=s.length()-1;
        while(i<j){
            if(s.charAt(i)!=s.charAt(j))
                return false;
            ++i;
            --j;
        }
        return true;
    }
    static void update(int s,int e,int l,int r,int in,int v){
        if(s>e||s>r||l>e)
            return;
        if(s>=l&&e<=r){
            seg[in]=v;
            return;
        }
        int mid=(s+e)/2;
        update(s,mid,l,r,2*in+1,v);
        update(mid+1,e,l,r,2*in+2,v);
        seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
        static int query(int s,int e,int l,int r,int in){
        if(s>e||s>r||l>e)
            return 0;
        if(s>=l&&e<=r){
            return seg[in];
            
        }
        int mid=(s+e)/2;
        return Math.max(query(s,mid,l,r,2*in+1),
        query(mid+1,e,l,r,2*in+2));
        //seg[in]=Math.max(seg[2*in+1],seg[2*in+2]);
    }
    static double dist(long x,long y,long z,long w){
        return Math.sqrt((x-y)*(x-y)+(z-w)*(z-w));
    }
    static void add(int x,int y,Queue<Integer>q,Queue<Integer>v,int b[][]){
        q.add(x);
        v.add(y);
        b[x][y]=1;
    }
    static long nCr(long n, long r, 
                                    long p) 
    { 
        return (fac[(int)n]* modInverse(fac[(int)r], p) 
                % p * modInverse(fac[(int)(n-r)], p) 
                                    % p) % p; 
    } 
    //static int prime[];
    //static int dp[];
    public static void main(String[] args){
        //long sum=0;
        try {
                codeforces.solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
    }
       static long modInverse(long n, long p) 
    { 
        return power(n, p-(long)2,p); 
    } 
 static long power(long x, long y, long p) 
{ 
    long res = 1;      // Initialize result 
  
    x = x % p;  // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y %(long)2!=0) 
            res = (res*x) % p; 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x) % p;   
    } 
    return res%p;
 }
    /*public static long power(long x,long a) {
		if(a==0) return 1;
		if(a%2==1)return (x*1L*power(x,a-1))%mod;
		return (power((int)((x*1L*x)%mod),a/2))%mod;
	}*/
   static int find(int x) 
    { 
        // Finds the representative of the set 
        // that x is an element of 
        while(parent[x]!=x) 
        { 
            // if x is not the parent of itself 
            // Then x is not the representative of 
            // his set,
            x=parent[x];
  
            // so we recursively call Find on its parent 
            // and move i's node directly under the 
            // representative of this set 
        } 
  
        return x; 
    }
    static void union(int x, int y) 
    { 
        // Find representatives of two sets 
        int xRoot = find(x), yRoot = find(y); 
  
        // Elements are in the same set, no need 
        // to unite anything. 
        if (xRoot == yRoot) 
            return; 
  
         // If x's rank is less than y's rank 
        if (rank[xRoot] < rank[yRoot]) 
  
            // Then move x under y  so that depth 
            // of tree remains less 
            parent[xRoot] = yRoot; 
  
        // Else if y's rank is less than x's rank 
        else if (rank[yRoot] < rank[xRoot]) 
  
            // Then move y under x so that depth of 
            // tree remains less 
            parent[yRoot] = xRoot; 
  
        else // if ranks are the same 
        { 
            // Then move y under x (doesn't matter 
            // which one goes where) 
            parent[yRoot] = xRoot; 
  
            // And increment the the result tree's 
            // rank by 1 
            rank[xRoot] = rank[xRoot] + 1; 
        } 
    } 
    static long gcd(long a, long b) 
    { 
        if (a == 0){ 
             //ans+=b;
            return b;
        }
        return gcd(b % a, a); 
    }
}