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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader;

public class CountSubrectangles{

    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; 
        } 
    }
    public static void main(String[] args){
        FastReader s = new FastReader();
        int n = s.nextInt();
        int m = s.nextInt();
        int k = s.nextInt();
        int[] na = new int[n+1];
        int[] ma = new int[m+1];
        for(int i = 1;i<=n;i++){
            na[i] = s.nextInt() + na[i-1];
        }
        // for(int i = 1;i<=n;i++){
        //     System.out.print(na[i] + " ");
        // }
        for(int j = 1;j<=m;j++){
            ma[j] = s.nextInt() + ma[j-1];  
        }
        // for(int i = 1;i<=m;i++){
        //     System.out.print(ma[i]+" ");
        // }
        ArrayList<Integer> divisors = new ArrayList<>();
        for(int i = 1;i*i<=k;i++){
            if(k%i==0){
                divisors.add(i);
                if(i*i<k) divisors.add(k/i);
            }
        }
        long ans = 0;
        for(int i = 0;i<divisors.size();i++){
            int curr = divisors.get(i);
            long x=0, y=0;
            for(int j = 1;j<=n-curr+1;j++){
                if(na[j+curr-1]-na[j-1]==curr){
                    x++;
                }
            }
            curr = k/curr;
            for(int j = 1;j<=m-curr+1;j++){
                if(ma[j+curr-1]-ma[j-1]==curr){
                    y++;
                }
            }
            ans+=x*y;
        }
        System.out.println(ans);
    }

}