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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
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
 *
 * @author unknown
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BCountSubrectangles solver = new BCountSubrectangles();
        solver.solve(1, in, out);
        out.close();
    }

    static class BCountSubrectangles {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int k = in.nextInt();
            int[] arr = new int[n + 2];
            int[] brr = new int[m + 2];
            arr[0] = arr[n + 1] = 0;
            brr[0] = brr[m + 1] = 0;
            for (int i = 1; i <= n; i++) {
                arr[i] = in.nextInt();
            }
            for (int i = 1; i <= m; i++) {
                brr[i] = in.nextInt();
            }
            int[] subsA = new int[n + 1];
            int[] subsB = new int[m + 1];
            int last = 0;
            for (int i = 1; i < n + 2; i++) {
                if (arr[i] == 0) {
                    int sublen = i - last - 1;
                    for (int j = 1; j <= sublen; j++) {
                        subsA[j] += (sublen - j + 1);
                    }
                    last = i;
                }
            }
            last = 0;
            for (int i = 1; i < m + 2; i++) {
                if (brr[i] == 0) {
                    int sublen = i - last - 1;
                    for (int j = 1; j <= sublen; j++) {
                        subsB[j] += (sublen - j + 1);
                    }
                    last = i;
                }
            }
            ArrayList<Integer> factors = _F.getDivisors(k);
            Collections.sort(factors);
            long ans = 0;
            for (int factr : factors) {
                if (factr <= n && k / factr <= m)
                    ans += (subsA[factr] * subsB[k / factr]);
            }
            out.println(ans);
        }

    }

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

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

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

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }

    static class _F {
        public static ArrayList<Integer> getDivisors(int n) {
            ArrayList<Integer> factors = new ArrayList<>();
            for (int i = 1; i * i <= n; i++) {
                if (n % i == 0) {
                    if (n / i == i) {
                        factors.add(i);
                    } else {
                        factors.add(i);
                        factors.add(n / i);
                    }
                }
            }
            return factors;
        }

    }
}

