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

public class Main {
    static PrintWriter out = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    int k;
    long[] d;
    public static void main(String[] args) throws IOException {
        Main main = new Main();
//        main.solve();
        System.out.println(main.solve());
    }
    long solve() throws IOException{
        int n = sc.nextInt(), m = sc.nextInt();
        long k = sc.nextLong();
        int[] a = new int[n], b = new int[m];
        for(int i=0;i<n;i++) a[i] = sc.nextInt();
        for(int i=0;i<m;i++) b[i] = sc.nextInt();
        List<Integer> col = helper(a,n),row = helper(b,m);
        Set<Long> divisors = new HashSet<>();
        for(long i=1;i*i<=k;i++){
            if(k%i==0){
                divisors.add(i); divisors.add(k/i);
            }
        }
        long ans = 0;
        for(long w:divisors){
            long h = k/w;
            long sumRow = 0;
            for(int i:row){
                if(i>=w) sumRow += i+1-w;
            }
            for(int j:col){
                if(j>=h){
                    long cur = j+1-h;
                    ans += cur*sumRow;
                }
            }
        }
        return ans;
    }
    List<Integer> helper(int[] a, int n){
        List<Integer> ans = new ArrayList<>();
        int left = 0;
        while(left<n){
            if(a[left]==0) {
                left++;
                continue;
            }
            int right = left;
            while(right<n&&a[right]==1) right++;
            ans.add(right-left);
            left = right;
        }
        return ans;
    }
}

