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 egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict Not sended
 * @url https://codeforces.com/problemset/problem/
 * @category ?
 * @date 21/05/2020
 **/

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

import static java.lang.Integer.*;
import static java.lang.Math.*;

public class CFB {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        for (String ln; (ln = in.readLine()) != null && !ln.equals(""); ) {
            StringTokenizer st = new StringTokenizer(ln);
            int N = parseInt(st.nextToken()), M = parseInt(st.nextToken()), K = parseInt(st.nextToken());
            int A[] = new int[N];
            int B[] = new int[M];
            long QA[] = new long[N + 1];
            long QB[] = new long[M + 1];
            st = new StringTokenizer(in.readLine());
            for (int i = 0; i < N; i++) {
                A[i] = parseInt(st.nextToken());
            }
            st = new StringTokenizer(in.readLine());
            for (int i = 0; i < M; i++) {
                B[i] = parseInt(st.nextToken());
            }
            f(A, QA);
            f(B, QB);
            long s = 0;
            for (int i = 1; i < QA.length; i++)
                if (K % i == 0 && K / i < QB.length)
                    s += QA[i] * QB[K / i];
            System.out.println(s);
        }
    }

    static void f(int[] A, long[] Q) {
        int s = 0;
        for (int i = 0; i < A.length; i++) {
            if (A[i] == 1) {
                s++;
            } else if (s > 0) {
                Q[s]++;
                s = 0;
            }
        }
        if (s > 0) Q[s]++;
        for (int i = Q.length - 2; i > 0; i--)
            Q[i] += Q[i + 1] * 2 - (i < Q.length - 2 ? Q[i + 2] : 0);
    }
}

