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 Test {
//

//    private static int c = 1000010;
    private static int r = 1000_000_007;

    public static void main(String[] args) {
//        Scanner in = new Scanner(System.in);
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(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 i = 0; i < m; i++) {
            b[i] = in.nextInt();
        }
        Map<Integer, Integer> mapa = new HashMap<>();
        int l = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] == 1) {
                l++;
            } else if (l != 0) {
                mapa.put(l, mapa.getOrDefault(l, 0) + 1);
                l = 0;
            }
        }
        if (l != 0) {
            mapa.put(l, mapa.getOrDefault(l, 0) + 1);
        }
        Map<Integer, Integer> mapb = new HashMap<>();
        l = 0;
        for (int i = 0; i < m; i++) {
            if (b[i] == 1) {
                l++;
            } else if (l != 0) {
                mapb.put(l, mapb.getOrDefault(l, 0) + 1);
                l = 0;
            }
        }
        if (l != 0) {
            mapb.put(l, mapb.getOrDefault(l, 0) + 1);
        }
        Set<Integer> al = mapa.keySet();
        Set<Integer> bl = mapb.keySet();

        l = (int) Math.sqrt(k);
        int[] pairs = new int[l + 1];
        for (int i = 1; i <= l; i++) {
            if (k % i == 0) {
                pairs[i] = k / i;
            }
        }
        
        long ans = 0;
        for (Integer r : al) {
            for (Integer c : bl) {
                for (int i = 1; i <= l; i++) {
                    if (pairs[i] != 0) {
                        if (i <= r && pairs[i] <= c) {
                            ans += (r - i + 1) * (c - pairs[i] + 1) * mapa.get(r) * mapb.get(c);
                        }
                        if (i <= c && pairs[i] <= r) {
                            ans += (c - i + 1) * (r - pairs[i] + 1) * mapa.get(r) * mapb.get(c);
                        }
                    }
                }
                if (pairs[l] == l && l <= r && l <= c) {
                    ans -= (r - l + 1) * (c - l + 1) * mapa.get(r) * mapb.get(c);
                }
            }
        }
        System.out.println(ans);

    }
}

class FastScanner {

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

    String next() {
        while (!st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

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

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