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.Arrays;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class Main {
    private FastScanner in;
    private PrintWriter out;

    public static void main(String[] args) {
        (new Main()).run();
    }

    private void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solution();
        } catch (Exception e) {
            e.printStackTrace();
        } finally {
            if (in != null) {
                try {
                    in.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            if (out != null) out.close();
        }
    }

    private void solution() throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        int[] a = readIntArray(n);
        int[] b = readIntArray(m);
        int[] resA = getValue(a, k);
        int[] resB = getValue(b, k);
        //printIntArray(resA);
        long res = 0;
        for (int i = 1; i < resA.length && resA[i] > 0; i++) {
            if (k % i == 0) {
                int need = k / i;
                long have = need < resB.length ? resB[need] : 0;
                res += have * resA[i];
            }
        }
        out.println(res);
    }

    private int[] readIntArray(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = in.nextInt();
        }
        return res;
    }

    private void printIntArray(int[] array) {
        out.println(Arrays.stream(array).boxed().map(String::valueOf).collect(Collectors.joining(", ")));
    }

    private int[] getValue(int[] array, int k) {
        int[] res = new int[array.length + 1];
        int cur = 0;
        for (int val : array) {
            if (val == 0) {
                cur = 0;
            } else {
                cur++;
                res[cur]++;
            }
        }
        for (int i = array.length - 1; i > 0; i--) {
            res[i] += res[i + 1];
        }
        return res;
    }

    private class FastScanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String temp = bufferedReader.readLine();
                if (temp == null) {
                    return null;
                }
                stringTokenizer = new StringTokenizer(temp);
            }
            return stringTokenizer.nextToken();
        }

        String nextLine() throws IOException {
            return bufferedReader.readLine();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(this.next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(this.next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(this.next());
        }

        void close() throws IOException {
            bufferedReader.close();
        }
    }
}