You are given an array a of length n and array b of length m both consisting of only integers 0 and 1. Consider a matrix c of size n × m formed by following rule: c_{i, j} = a_i ⋅ b_j (i.e. a_i multiplied by b_j). It's easy to see that c consists of only zeroes and ones too.

How many subrectangles of size (area) k consisting only of ones are there in c?

A subrectangle is an intersection of a consecutive (subsequent) segment of rows and a consecutive (subsequent) segment of columns. I.e. consider four integers x_1, x_2, y_1, y_2 (1 ≤ x_1 ≤ x_2 ≤ n, 1 ≤ y_1 ≤ y_2 ≤ m) a subrectangle c[x_1 ... x_2][y_1 ... y_2] is an intersection of the rows x_1, x_1+1, x_1+2, ..., x_2 and the columns y_1, y_1+1, y_1+2, ..., y_2.

The size (area) of a subrectangle is the total number of cells in it.

Input

The first line contains three integers n, m and k (1 ≤ n, m ≤ 40 000, 1 ≤ k ≤ n ⋅ m), length of array a, length of array b and required size of subrectangles.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 1), elements of a.

The third line contains m integers b_1, b_2, …, b_m (0 ≤ b_i ≤ 1), elements of b.

Output

Output single integer — the number of subrectangles of c with size (area) k consisting only of ones.

Examples

Input


3 3 2
1 0 1
1 1 1


Output


4


Input


3 5 4
1 1 1
1 1 1 1 1


Output


14

Note

In first example matrix c is:

<image>

There are 4 subrectangles of size 2 consisting of only ones in it:

<image>

In second example matrix c is:

<image>
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int m = s.nextInt();
		int k = s.nextInt();
		int[] a = new int[n];
		int[] b = new int[m];
		for(int i=0;i<n;i++){
		    a[i] = s.nextInt();
		}
		for(int i=0;i<m;i++){
		    b[i] = s.nextInt();
		}
		int[] row = new int[n];
		int[] col = new int[m];
		if(a[0]==1) row[0]=1;
		if(b[0]==1) col[0]=1;
		for(int i=1;i<n;i++){
		    if(a[i]==1){
		        if(a[i-1]==1) row[i]=1+row[i-1];
		        else row[i]=1;
		    }
		}
		for(int i=1;i<m;i++){
		    if(b[i]==1){
		        if(b[i-1]==1) col[i]=1+col[i-1];
		        else col[i]=1;
		    }
		}
		Arrays.sort(col);
		Arrays.sort(row);
		long ans=0;
		long temp=0;
		for(int i=1;i*i<=k;i++){
		    if(k%i==0){
		        if(i*i==k){
		            temp= (n-bsearch(0,n-1,row,i)-1);
		            temp*=(m-bsearch(0,m-1,col,i)-1);
		            ans+=temp;
		        }
		        else{
		            temp=(n-bsearch(0,n-1,row,i)-1);
		            temp*=(m-bsearch(0,m-1,col,k/i)-1);
		            ans+=temp;
		            temp=(n-bsearch(0,n-1,row,k/i)-1);
		            temp*=(m-bsearch(0,m-1,col,i)-1);
		            ans+=temp;
		        }
		    }
	    }
	    System.out.println(ans);
	}
	public static int bsearch(int i,int j,int[] a,int t){
	    if(i>j) return i;
	    if(i==j){
	        if(a[i]<t) return i;
	        else return i-1;
	    }
	    int mid = (i+j)/2;
	    if(a[mid]==t){
	        mid--;
	        while(mid>=0&&a[mid]==t) mid--;
	        return mid;
	    }
	    else if(a[mid]>t) j=mid-1;
	    else i = mid+1;
	    return bsearch(i,j,a,t);
	}
}
