Problem: How many stars are there in the sky? A young programmer Polycarpus can't get this question out of his head! He took a photo of the starry sky using his digital camera and now he analyzes the resulting monochrome digital picture. The picture is represented by a rectangular matrix consisting of n lines each containing m characters. A character equals '1', if the corresponding photo pixel is white and '0', if it is black.

Polycarpus thinks that he has found a star on the photo if he finds a white pixel surrounded by four side-neighboring pixels that are also white: 
    
    
      
     1   
    111  
     1   
    

a star on the photo

Polycarpus whats to cut out a rectangular area from the photo and give his mom as a present. This area should contain no less than k stars. The stars can intersect, have shared white pixels on the photo. The boy will cut out the rectangular area so that its borders will be parallel to the sides of the photo and the cuts will go straight between the pixel borders.

Now Polycarpus keeps wondering how many ways there are to cut an area out of the photo so that it met the conditions given above. Help Polycarpus find this number.

Input

The first line of the input data contains three integers n, m and k (1 ≤ n, m ≤ 500;1 ≤ k ≤ nm). Then follow n lines, containing the description of the given photo as a sequence of lines. Each line contains m characters '0' or '1'.

Output

Print the required number of areas on the given photo.

Examples

Input

4 6 2
111000
111100
011011
000111


Output

6


Input

5 5 4
11111
11111
11111
11111
11111


Output

9

Note

We'll number the rows and columns below starting from 1, the coordinates (p, q) will denote a cell in row p, column q.

In the first sample Polycarpus should cut out any area containing a rectangle whose opposite corners lie in cells (1, 1) and (3, 4). Only rectangles with opposite corners in (1, 1) and (x, y), where x ≥ 3 and y ≥ 4 fit the conditions.

In the second sample any rectangle whose each side is no less than four, will do. The possible rectangle sizes are 4 × 4, 4 × 5, 5 × 4 and 5 × 5. Such figures can be cut in 4 ways, 2 ways, 2 ways and 1 way correspondingly.

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use cin, cout streams or the %I64d specificator.

Solution (in JAVA):

Solution:
// Don't place your source in a package
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*; 
 
 /*
 
 6666666666666			 6666666666666                     
 6						 6  											   			
 6						 6                                      
 6						 6                                      
 6						 6                                       
 6                       6                                                 
 6666666666666           6666666666666                     
 6		     6           6		     6
 6			 6	         6			 6 
 6			 6           6			 6
 6		     6	         6		     6	
 6666666666666           6666666666666
 

 */
 
 
 
 
 
// Please name your class Main
public class Main {
	
	//static StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
 
    /*static int read() throws IOException {
        in.nextToken();
        return (int) in.nval;
    }
    static String readString() throws IOException {
        in.nextToken();
        return in.sval;
	}*/
	
	
	static Scanner in = new Scanner(System.in);
	
	public static void main (String[] args) throws java.lang.Exception {
	    
		//InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
 
		int T=1;
		
		for(int t=0;t<T;t++){
			int n=Int();
			int m=Int();
			int k=Int();
			int A[][]=new int[n][m];
			for(int i=0;i<n;i++){
				String s=Str();
				for(int j=0;j<m;j++){
					A[i][j]=s.charAt(j)-'0';
				}
			}
			
			Solution sol=new Solution();
			sol.solution(k,A);
		}
 
		out.flush();
	}
 
	public static int Int(){
		return in.nextInt();
	}
	public static String Str(){
		return in.next();
	}
}
 
class Solution{
	//constant variable
	final int MAX=Integer.MAX_VALUE;
	final int MIN=Integer.MIN_VALUE;
	//Set<Integer>adjecent[];
	//////////////////////////////
 
	

	public void solution(int k,int A[][]){  
		int R=A.length;
		int C=A[0].length;
		long res=0;
		int grid[][]=new int[A.length][A[0].length];
		int dp[][]=new int[A.length][A[0].length];
		for(int i=1;i<A.length-1;i++){
			for(int j=1;j<A[0].length-1;j++){
				if(A[i][j]==1&&A[i-1][j]==1&&A[i+1][j]==1&&A[i][j-1]==1&&A[i][j+1]==1){
					grid[i][j]=1;
				}
			}
		}
		//find how many submatrix sum>=K
		
		for(int i=0;i<grid.length;i++){
			int sum=0;
			for(int j=0;j<grid[0].length;j++){
				sum+=grid[i][j];
				dp[i][j]=sum;
			}
		}
		
		//print2(grid);
		//msg("");
		//print2(dp);
		
		for(int c=1;c<A[0].length-1;c++){
			for(int pre=c;pre>=1;pre--){
				Queue<Integer>q=new LinkedList<>();
				int sum=0;
				for(int r=1;r<A.length;r++){
					int cur=dp[r][c]-get1(dp,r,pre-1);
					
					sum+=cur;
					q.add(cur);
					while(q.size()>0&&sum>=k){
						int add=R-(r+1);
						//msg(r+"  "+c+"  "+cur+"  "+add);
						res+=add;
						sum-=q.poll();
					}
				}
				
			}
			
		}
		
		msg(res+"");
	}
		
	public int get1(int A[][],int i,int j){
		if(i<0||j<0)return 0;
		return A[i][j];
	}
	
	

	
	
	

	
	


	
	
		
	
	public void swap(int A[],int l,int r){
		int t=A[l];
		A[l]=A[r];
		A[r]=t;
	}
	

	
	
	public long C(long fact[],int i,int j){ // C(20,3)=20!/(17!*3!)
		// take   a/b     where a=20!  b=17!*3!
		if(j>i)return 0;
		if(j==0)return 1;
		long mod=1000000007;
		long a=fact[i];
		long b=((fact[i-j]%mod)*(fact[j]%mod))%mod;
		BigInteger B= BigInteger.valueOf(b);
		long binverse=B.modInverse(BigInteger.valueOf(mod)).longValue();
		return ((a)*(binverse%mod))%mod;
	}
	
	
	 
	
	//map operation
	public void put(Map<Integer,Integer>map,int i){
		if(!map.containsKey(i))map.put(i,0);
		map.put(i,map.get(i)+1);
	}
	
	public void delete(Map<Integer,Integer>map,int i){
		map.put(i,map.get(i)-1);
		if(map.get(i)==0)map.remove(i);
	}
 
 
 
 
 
	
 
 
	/*public void tarjan(int p,int r){
		if(cut)return;
		List<Integer>childs=adjecent[r];
		dis[r]=low[r]=time;
		time++;
		
		//core for tarjan
		int son=0;
		for(int c:childs){
			if(ban==c||c==p)continue;
			if(dis[c]==-1){
				son++;
				tarjan(r,c);
				low[r]=Math.min(low[r],low[c]);
				if((r==root&&son>1)||(low[c]>=dis[r]&&r!=root)){
					cut=true;
					return;
				}
			}else{
				if(c!=p){
					low[r]=Math.min(low[r],dis[c]);
				}
			}
		}
		
	}*/
	
	
 
	
	//helper function I would use
	public void remove(Map<Integer,Integer>map,int i){
		map.put(i,map.get(i)-1);
		if(map.get(i)==0)map.remove(i);
	}
	
	
	
	public void ascii(String s){
		for(char c:s.toCharArray()){
			System.out.print((c-'a')+" ");
		}
		msg("");
	}
	
	public int flip(int i){
		if(i==0)return 1;
		else return 0;
	}
	
	public boolean[] primes(int n){
		boolean A[]=new boolean[n+1];
		for(int i=2;i<=n;i++){
			if(A[i]==false){
				for(int j=i+i;j<=n;j+=i){
					A[j]=true;
				}
			}
		}
		return A;
	}
	
	public void msg(String s){
		System.out.println(s);
	}
	
	public void msg1(String s){
		System.out.print(s);
	}
	
	public int[] kmpPre(String p){
		int pre[]=new int[p.length()];
		int l=0,r=1;
		while(r<p.length()){
			if(p.charAt(l)==p.charAt(r)){
				pre[r]=l+1;
				l++;r++;
			}else{
				if(l==0)r++;
				else l=pre[l-1];
			}
		}
		return pre;
	}
	
	public boolean isP(String s){
		int l=0,r=s.length()-1;
		while(l<r){
			if(s.charAt(l)!=s.charAt(r))return false;
			l++;r--;
		}
		return true;
	}
	
	public int find(int nums[],int x){//union find => find method
		if(nums[x]==x)return x;
		int root=find(nums,nums[x]);
		nums[x]=root;
		return root;
	}
	
 
	
	public int get(int A[],int i){
		if(i<0||i>=A.length)return 0;
		return A[i];
	}
	public int[] copy1(int A[]){
		int a[]=new int[A.length];
		for(int i=0;i<a.length;i++)a[i]=A[i];
		return a;
	}
	
	
	public void print1(int A[]){
		for(long i:A)System.out.print(i+" ");
		System.out.println();
	}
	public void print2(int A[][]){
		for(int i=0;i<A.length;i++){
			for(int j=0;j<A[0].length;j++){
				System.out.print(A[i][j]+" ");
			}System.out.println();
		}
	}
	
	public int min(int a,int b){
		return Math.min(a,b);
	}
	
	
	public int[][] matrixdp(int[][] grid) {
        if(grid.length==0)return new int[][]{};
        int res[][]=new int[grid.length][grid[0].length];
        for(int i=0;i<grid.length;i++){
            for(int j=0;j<grid[0].length;j++){
                res[i][j]=grid[i][j]+get(res,i-1,j)+get(res,i,j-1)-get(res,i-1,j-1);
            }
        }
        return res;
    }
    
    public int get(int grid[][],int i,int j){
        if(i<0||j<0||i>=grid.length||j>=grid[0].length)return 0;
        return grid[i][j];
    }
	
	public int[] suffixArray(String s){
		int n=s.length();
		Suffix A[]=new Suffix[n];
		
		for(int i=0;i<n;i++){
			A[i]=new Suffix(i,s.charAt(i)-'a',0);
		}
		
		for(int i=0;i<n;i++){
			if(i==n-1){
				A[i].next=-1;
			}else{
				A[i].next=A[i+1].rank;
			}
		}
		Arrays.sort(A);
		
		for(int len=4;len<A.length*2;len<<=1){
			int in[]=new int[A.length];
			int rank=0;
			int pre=A[0].rank;
			A[0].rank=rank;
			in[A[0].index]=0;
			for(int i=1;i<A.length;i++){//rank for the first two letter
				if(A[i].rank==pre&&A[i].next==A[i-1].next){
					pre=A[i].rank;
					A[i].rank=rank;
				}else{
					pre=A[i].rank;
					A[i].rank=++rank;
				}
				in[A[i].index]=i;
			}
			
			for(int i=0;i<A.length;i++){
				int next=A[i].index+len/2;
				if(next>=A.length){
					A[i].next=-1;
				}else{
					A[i].next=A[in[next]].rank;
				}
			}
			
			
			Arrays.sort(A);
		}
		
		
		int su[]=new int[A.length];
		for(int i=0;i<su.length;i++){
			su[i]=A[i].index;
		}
		return su;
	}
	
}
 
//suffix array Struct
class Suffix implements Comparable<Suffix>{
	int index;
	int rank;
	int next;
	public Suffix(int i,int rank,int next){
		this.index=i;
		this.rank=rank;
		this.next=next;
	}
	
	@Override
	public int compareTo(Suffix other) {
		if(this.rank==other.rank){
			return this.next-other.next;
		}
		return this.rank-other.rank;
	}
	
	public String toString(){
		return this.index+"   "+this.rank+"   "+this.next+"  ";
	}
}
 
 
 
class Wrapper implements Comparable<Wrapper>{
	int spf;int cnt;
	public Wrapper(int spf,int cnt){
		this.spf=spf;
		this.cnt=cnt;
	}
		
	@Override
	public int compareTo(Wrapper other) {
		return this.spf-other.spf;
	}
}
 
 
 
    class Node{//what the range would be for that particular node
		boolean state=false;
        int l=0,r=0;
		int ll=0,rr=0;
        public Node(boolean state){
            this.state=state;
        }
    }
	
	
	
	
	class Seg1{
			int A[];
			public Seg1(int A[]){
				this.A=A;
			}
			
			public void update(int left,int right,int val,int s,int e,int id){
				if(left<0||right<0||left>right)return;
				if(left==s&&right==e){
					
					A[id]+=val;
					return;
				}
				int mid=s+(e-s)/2; //[s,mid] [mid+1,e]
				
				if(left>=mid+1){
					update(left,right,val,mid+1,e,id*2+2);
				}else if(right<=mid){
					update(left,right,val,s,mid,id*2+1);
				}else{
					update(left,mid,val,s,mid,id*2+1);
					update(mid+1,right,val,mid+1,e,id*2+2);
				}
			}
			
			public int query(int i,int add,int s,int e,int id){
				
				if(s==e&&i==s){
					return A[id]+add;
				}
				
				int mid=s+(e-s)/2; //[s,mid] [mid+1,e]
				
				if(i>=mid+1){
					return query(i,A[id]+add,mid+1,e,id*2+2);
				}else{
					return query(i,A[id]+add,s,mid,id*2+1);
				}
			}
	}
 
 
	 class MaxFlow{
		
 
		  public static List<Edge>[] createGraph(int nodes) {
			List<Edge>[] graph = new List[nodes];
			for (int i = 0; i < nodes; i++)
			  graph[i] = new ArrayList<>();
			return graph;
		  }
 
		  public static void addEdge(List<Edge>[] graph, int s, int t, int cap) {
			graph[s].add(new Edge(t, graph[t].size(), cap));
			graph[t].add(new Edge(s, graph[s].size() - 1, 0));
		  }
 
		  static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
			Arrays.fill(dist, -1);
			dist[src] = 0;
			int[] Q = new int[graph.length];
			int sizeQ = 0;
			Q[sizeQ++] = src;
			for (int i = 0; i < sizeQ; i++) {
			  int u = Q[i];
			  for (Edge e : graph[u]) {
				if (dist[e.t] < 0 && e.f < e.cap) {
				  dist[e.t] = dist[u] + 1;
				  Q[sizeQ++] = e.t;
				}
			  }
			}
			return dist[dest] >= 0;
		  }
 
		  static int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
			if (u == dest)
			  return f;
			for (; ptr[u] < graph[u].size(); ++ptr[u]) {
			  Edge e = graph[u].get(ptr[u]);
			  if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
				int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
				if (df > 0) {
				  e.f += df;
				  graph[e.t].get(e.rev).f -= df;
				  return df;
				}
			  }
			}
			return 0;
		  }
 
		  public static int maxFlow(List<Edge>[] graph, int src, int dest) {
			int flow = 0;
			int[] dist = new int[graph.length];
			while (dinicBfs(graph, src, dest, dist)) {
			  int[] ptr = new int[graph.length];
			  while (true) {
				int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
				if (df == 0)
				  break;
				flow += df;
			  }
			}
			return flow;
		  }
		 
	 }
	 
	 	 class Edge {
			int t, rev, cap, f;
 
			public Edge(int t, int rev, int cap) {
			  this.t = t;
			  this.rev = rev;
			  this.cap = cap;
			}
		  }
		  
		  
		  
		  
		  
		  
    class Seg{
        int l,r;
        int min=Integer.MAX_VALUE;
        Seg left=null,right=null;
        public Seg(int l,int r){
            this.l=l;
            this.r=r;
            if(l!=r){
                int mid=l+(r-l)/2;
                if(l<=mid)left=new Seg(l,mid);
                if(r>=mid+1)right=new Seg(mid+1,r);
                if(left!=null)min=Math.min(left.min,min);
                if(right!=null)min=Math.min(right.min,min);
            }else{
                min=10000000;
            }
        }
        public int query(int s,int e){
            if(l==s&&r==e){
                return min;
            }
            int mid=l+(r-l)/2; //left :  to mid-1,
            if(e<=mid){
                return left.query(s,e);
            }
            else if(s>=mid+1){
                return right.query(s,e);
            }else{
                return Math.min(left.query(s,mid),right.query(mid+1,e));
            }
        }

        public void update(int index,int v){
            if(l==r){
                min=Math.min(min,v);
                return;
            }
            int mid=l+(r-l)/2;
            if(index<=mid){
                left.update(index,v);
            }else{
                right.update(index,v);
            }
            this.min=Math.min(left.min,right.min);
        }
    }