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>
import java.util.*;
import java.io.*;
public class A
{
    public static void main(String ar[]) throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String s1[]=br.readLine().split(" ");
        int n=Integer.parseInt(s1[0]);
        int m=Integer.parseInt(s1[1]);
        int k=Integer.parseInt(s1[2]);
        
        int a[]=new int[n];
        String s2[]=br.readLine().split(" ");
        for(int i=0;i<n;i++)
         a[i]=Integer.parseInt(s2[i]);
        
        for(int i=1;i<n;i++)
        {
            if(a[i]!=0)
             a[i]+=a[i-1];
        }
        
        int b[]=new int[m];
        String s3[]=br.readLine().split(" ");
        for(int i=0;i<m;i++)
         b[i]=Integer.parseInt(s3[i]);
        
        for(int i=1;i<m;i++)
        {
            if(b[i]!=0)
             b[i]+=b[i-1];
        }
        
        long t=0;
        for(int i=1;i<=Math.sqrt(k);i++)
        {
            if(k%i!=0)
             continue;
            
            int x=0,y=0;
            int v=k/i;
            for(int j=0;j<n;j++)
             if(a[j]>=i)
              x++;
            for(int j=0;j<m;j++)
             if(b[j]>=v)
              y++;
            
            t+=(long)x*y;
            if(i==v)
             continue;
            x=0; y=0;
            
            for(int j=0;j<n;j++)
             if(a[j]>=v)
              x++;
            for(int j=0;j<m;j++)
             if(b[j]>=i)
              y++;
            
            t+=(long)x*y;
        }
        
        System.out.println(t);
    }
}