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.*;

public class Main {
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);

        int n = nextInt();
        int m = nextInt();
        int k = nextInt();

        int[] a = new int[n];
        int[] b = new int[m];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        for (int i = 0; i < m; i++) {
            b[i] = nextInt();
        }

        TreeSet<Integer> ts = new TreeSet<>();
        for (int i = 1; i * i <= k; i++) {
            if (k % i == 0) {
                ts.add(i);
                if (k / i != i) ts.add(k / i);
            }
        }

        int[] first = new int[ts.size()];
        int[] second = new int[ts.size()];
        int id = 0;

        for (int x : ts) {
            int j = 0;
            int cnt = 0;
            for (int i = 0; i < n; ) {
                if (a[i] == 0) {
                    i++;
                    j = i;
                } else {
                    if (a[j] == 1) {
                        if (j - i + 1 == x) {
                            i++;
                            cnt++;
                        }
                        j++;
                        if (j >= n) break;
                    } else i = j;
                }
            }
            first[id] = cnt;
            id++;
        }
        id = 0;
        for (int x : ts) {
            int j = 0;
            int cnt = 0;
            for (int i = 0; i < m; ) {
                if (b[i] == 0) {
                    i++;
                    j = i;
                } else {
                    if (b[j] == 1) {
                        if (j - i + 1 == x) {
                            i++;
                            cnt++;
                        }
                        j++;
                        if (j >= m) break;
                    } else i = j;
                }
            }
            second[id] = cnt;
            id++;
        }
        long answer = 0;
        for (int i = 0; i < ts.size(); i++) {
            answer += ((long) first[i] * (long) second[ts.size() - i - 1]);
        }
        pw.println(answer);
        pw.close();
    }

    static StringTokenizer st = new StringTokenizer("");
    static BufferedReader br;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

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

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

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