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.util.*;

public class main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		int[] a = new int[n + 1];
		int[] b = new int[m+1];

		for (int i = 1; i < a.length; i++) {
			a[i] = sc.nextInt();
			a[i] = a[i] + a[i - 1];
		}

		for (int j = 1; j < b.length; j++) {
			b[j] = sc.nextInt();
			b[j] = b[j] + b[j - 1];
		}

		// for divisors
		
		
		long ans = 0;
		for (int j = 1; j * j <= k; j++) {

			if (k % j == 0) {
				int x = k / j;
				int c1 = 0;
				int c2 = 0;
				int c3 = 0;
				int c4 = 0;

				// 1*4
				// 1
				for (int i = j; i < a.length; i++) {
					if (a[i] - a[i - j] == j) {
						c1++;
					}
				}

				// 4
				for (int i = x; i < b.length; i++) {
					if (b[i] - b[i - x] == x) {
						c2++;
					}
				}

				// 4
				for (int i = x; i < a.length; i++) {
				
					if (a[i] - a[i - x] == x) {
						c3++;
					}
				}

				// 1
				for (int i = j; i < b.length; i++) {
					if (b[i] - b[i - j] == j) {
						c4++;
					}
				}
				
				if (x == j) {
					ans = ans + c1 * c2;
				} else {
					ans = ans + c1 * c2 + c3 * c4;
				}
			}

		}
		System.out.println(ans);

	}

}
