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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author bhavy seth
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, InputReader sc, PrintWriter out) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int k = sc.nextInt();
            int a[] = new int[n];
            int b[] = new int[m];

            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
            }
            int noa[] = new int[n + 2];
            int nob[] = new int[m + 2];
            for (int i = 0; i < m; i++) {
                b[i] = sc.nextInt();
            }

            for (int i = 0; i < n; i++) {
                int len = 0;
                if (a[i] == 1) {
                    while (i < n && a[i] == 1) {
                        len++;
                        i++;
                        noa[1]++;
                        noa[len + 1]--;
                    }
                    i--;
                }
            }
            for (int i = 1; i <= n; i++) {
                noa[i] += noa[i - 1];
            }
            for (int i = 0; i < m; i++) {
                int len = 0;
                if (b[i] == 1) {
                    while (i < m && b[i] == 1) {
                        len++;
                        i++;
                        nob[1]++;
                        nob[len + 1]--;
                    }
                    i--;
                }
            }
            for (int i = 1; i <= m; i++) {
                nob[i] += nob[i - 1];
            }
            long res = 0;
            for (int i = 1; i <= n; i++) {
                if (k % i == 0) {
                    int x = k / i;
                    if (x <= m)
                        res += noa[i] * nob[x];
                }
            }
            out.println(res);

        }

    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

