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>
/******************************************
 *  Author : Atul Anand   
 *  Created On : Sat Mar 07 2020
 *******************************************/

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

public class B{
    
    public static void main(String[] args) throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        int a[] = new int[n];
        int b[] = new int[m];
        read(a, n);
        read(b, m);

        long count1[] = count(a, n);
        long count2[] = count(b, m);
        long ans = 0;
        for(int i = 1; i <= n; i++){
            // area k = i * k/i
            if(k % i == 0 && k/i <= m){
                ans += count1[i] * count2[k/i];
            }
        }
        println(ans);
        in.close();
        out.close();
    }

    static long[] count(int a[], int n){
        // count subarrays of 1s of all lengths
        long cnt[] = new long[n + 1];
        int streak = 0;
        for(int i = 0; i < n; i++){
            if(a[i] == 0){
                for(int j = 1; j <= streak; j++){
                    cnt[j] += streak - j + 1;
                }
                streak = 0;
            }
            else{
                streak++;
            }
        }
        
        for(int j = 1; j <= streak; j++){
            cnt[j] += streak - j + 1;
        }

        return cnt;
    }

    static int MIN = Integer.MIN_VALUE;
    static int MAX = Integer.MAX_VALUE;
    static Reader in = new Reader();
    static PrintWriter out = new PrintWriter(System.out);
    static void read(int arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.nextInt(); } }
    static void read(long arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.nextLong(); } }
    static void read(String arr[], int N) throws IOException{ for(int i = 0; i < N; i++){ arr[i] = in.next(); } }
    static void print(Object O){ out.print(O); }
    static void println(Object O){ out.println(O); }
    static void print(int arr[]){ for(int i = 0; i < arr.length; i++){ print(arr[i]+" "); } println(""); }
    static void print(int arr[][]){ for(int i = 0; i < arr.length; i++){ print(arr[i]); } }
    static void debug(Object O){ System.out.println(O); }
}

class Reader {
    BufferedReader reader;
    StringTokenizer tokenizer;

    Reader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    String next() throws IOException {
        while (!tokenizer.hasMoreTokens() ) { 
            tokenizer = new StringTokenizer(reader.readLine()); 
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException { 
        return Integer.parseInt(next()); 
    }
    
    double nextDouble() throws IOException { 
        return Double.parseDouble(next());
    }
    
    long nextLong() throws IOException { 
        return Long.parseLong(next()); 
    }
    
    String nextLine() throws IOException { 
        return reader.readLine(); 
    }
    
    void close() throws IOException { 
        reader.close(); 
    }
}