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.HashMap;
import java.io.IOException;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        BCountSubrectangles solver = new BCountSubrectangles();
        solver.solve(1, in, out);
        out.close();
    }

    static class BCountSubrectangles {
        PrintWriter out;
        InputReader in;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.out = out;
            this.in = in;
            int n = ni(), m = ni(), k = ni();
            ArrayList<Integer> div = new ArrayList<>();
            int i = 0;
            for (i = 1; i * i <= k; i++) {
                if (k % i == 0) {
                    div.add(i);
                    if (i != k / i)
                        div.add(k / i);
                }
            }
            int[] pf_1 = new int[n + 1];
            int[] pf_2 = new int[m + 1];
            for (i = 1; i <= n; i++)
                pf_1[i] += pf_1[i - 1] + ni();
            for (i = 1; i <= m; i++)
                pf_2[i] += pf_2[i - 1] + ni();
            Collections.sort(div);
            long[] count1 = new long[div.size()];
            long[] count2 = new long[div.size()];
            int j = 0;
            HashMap<Integer, Integer> hmap = new HashMap<>();
            for (int x : div) {
                for (i = 1; i <= n; i++) {
                    if (i + x - 1 > n)
                        break;
                    if (pf_1[i + x - 1] - pf_1[i - 1] == x)
                        count1[j]++;
                }
                for (i = 1; i <= m; i++) {
                    if (i + x - 1 > m)
                        break;
                    if (pf_2[i + x - 1] - pf_2[i - 1] == x)
                        count2[j]++;
                }
                hmap.put(x, j);
                j++;
            }
            long ans = 0;
            for (i = 1; i * i <= k; i++) {
                if (k % i == 0) {
                    ans += count1[hmap.get(i)] * count2[hmap.get(k / i)];
                    if (i != k / i)
                        ans += count1[hmap.get(k / i)] * count2[hmap.get(i)];
                }
            }
            pn(ans);
        }

        int ni() {
            return in.nextInt();
        }

        void pn(long zx) {
            out.println(zx);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

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

        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

