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.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class CountSubrectanglesNoFloodFill {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int k = sc.nextInt();
        List<Integer> rows = new ArrayList<>(N);
        for (int i = 0; i < N; i++) {
            int a = sc.nextInt();
            rows.add(a);
        }
        List<Integer> cols = new ArrayList<>(M);
        for (int i = 0; i < M; i++) {
            int a = sc.nextInt();
            cols.add(a);
        }
        int[] x = new int[N + 1];
        int count = 0;
        for (int i = 0; i < N; i++) {
            if (rows.get(i) == 1) {
                count++;
            }
            if (rows.get(i) == 0 || i == N - 1) {
                for (int j = 1; j <= count; j++) {
                    x[j] += count - j + 1;
                }
                count = 0;
            }

        }
        int[] y = new int[M + 1];
        count = 0;
        for (int i = 0; i < M; i++) {
            if (cols.get(i) == 1) {
                count++;
            }
            if (cols.get(i) == 0 || i == M - 1) {
                for (int j = 1; j <= count; j++) {
                    y[j] += count - j + 1;
                }
                count = 0;
            }

        }
        // System.out.println(Arrays.toString(x));
        // System.out.println(Arrays.toString(y));
        long sum = 0;
        for (int i = 1; i <= N; i++) {
            if (k % i == 0) {
                int c = k / i;
                if (c <= M) {
                    sum += x[i] * y[c];
                }
            }
        }
        out.println(sum);
        out.close();
    }

}
