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.*;


/**
 * Created by Katushka on 08.02.2020.
 */
public class CRM626B {

    static List<Integer> divs(int k) {
        int d = 1;
        List<Integer> ans = new ArrayList<>();
        while (d * d <= k) {
            if (k % d == 0) {
                ans.add(d);
                if (k / d != d) {
                    ans.add(k / d);
                }
            }

            d = d + 1;
        }
        return ans;
    }

    public static void main(String[] args) throws FileNotFoundException {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        int[] a = new int[n];
        int[] b = new int[m];

        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        for (int j = 0; j < m; j++) {
            b[j] = in.nextInt();
        }
        List<Integer> divs_k = divs(k);
        Collections.sort(divs_k);
        Map<Integer, Integer> b_intervals = getIntervals(m, b);
        Map<Integer, Integer> a_intervals = getIntervals(n, a);

        long ans = 0;
        for (Integer ai : a_intervals.keySet()) {
            for (Integer bi : b_intervals.keySet()) {
                int i = 0;
                long ans1 = 0;
                while (i < divs_k.size() && divs_k.get(i) <= ai) {
                    if (k / divs_k.get(i) <= bi) {
                        ans1 += ((long)(ai - divs_k.get(i) + 1)) * (bi - (k / divs_k.get(i)) + 1);
                    }
                    i++;

                }
                ans += ans1 * a_intervals.get(ai) * b_intervals.get(bi);
            }
        }
        out.println(ans);


        out.close();
    }

    private static Map<Integer, Integer> getIntervals(int n, int[] a) {
        int prev1;
        Map<Integer, Integer> intervals = new HashMap<>();
        prev1 = -1;
        for (int i = 0; i < n; i++) {
            if (a[i] == 0 && prev1 != -1) {
                int inter = i - 1 - prev1 + 1;
                if (intervals.containsKey(inter)) {
                    intervals.put(inter, intervals.get(inter) + 1);
                } else {
                    intervals.put(inter, 1);
                }
                prev1 = -1;
            }
            if (a[i] == 1 && prev1 == -1) {
                prev1 = i;
            }
        }
        if (prev1 != -1) {
            int inter = n - 1 - prev1 + 1;
            if (intervals.containsKey(inter)) {
                intervals.put(inter, intervals.get(inter) + 1);
            } else {
                intervals.put(inter, 1);
            }
        }
        return intervals;
    }


    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public char nextChar() {
            return next().charAt(0);
        }
    }
}
