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.stream.IntStream;
import java.util.List;
import java.util.Arrays;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * 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;
        Scanner in = new Scanner(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, Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            int M = in.nextInt();
            long K = in.nextLong();
            List<Pair> pairs = genPairs(K);
            int A[] = CPUtils.readIntArray(N, in);
            int B[] = CPUtils.readIntArray(M, in);

            long total = 0;
            for (Pair p : pairs)
            {
                total += getCount(p, A, B);
            }
            out.print(total);
        }

        private long getCount(Pair p, int[] a, int[] b)
        {
            long A = p.r;
            long B = p.c;
            return getConsecutives(A, a) * getConsecutives(B, b);
        }

        private long getConsecutives(long a, int[] a1)
        {
            if (a == 1) return Arrays.stream(a1).sum();
            long segments = 0;
            long partialCount = 0;
            for (int el : a1)
            {
                if (el == 1)
                {
                    partialCount++;
                    if (partialCount == a)
                    {
                        segments++;
                        partialCount--;
                    }
                } else
                {
                    partialCount = 0;
                }
            }
            return segments;
        }

        private List<Pair> genPairs(long k)
        {
            List<Pair> pairs = new ArrayList<>();
            if (k == 1)
            {
                pairs.add(new Pair(1L, 1L));
                return pairs;
            }
            for (long i = 1; i * i <= k; i++)
            {
                if (k % i == 0)
                {
                    pairs.add(new Pair(i, k / i));
                    if (i == (k / i)) continue;

                    pairs.add(new Pair(k / i, i));
                }
            }
            return pairs;
        }

    }

    static class Pair
    {
        long r;
        long c;

        Pair(long r, long c)
        {
            this.c = c;
            this.r = r;
        }

    }

    static class CPUtils
    {
        public static int[] readIntArray(int size, Scanner in)
        {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
            {
                array[i] = in.nextInt();
            }
            return array;
        }

    }
}

