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>
/*
javac b.java && java b
*/

import java.io.*;
import java.math.*;
import java.util.*;

public class b {
	public static void main(String[] args) { new b(); }
	FS in = new FS();
	PrintWriter out = new PrintWriter(System.out);

	int n, m, k;	
	int[] a, b;
	long ans;
	
	b() {
		n = in.nextInt();
		m = in.nextInt();
		k = in.nextInt();

		a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();
		b = new int[m];
		for (int i = 0; i < m; i++)
			b[i] = in.nextInt();
		
		ArrayList<Integer> pr = new ArrayList<>();
		for (int i = 1; i * i <= k; i++)
			if (k % i == 0) {
				pr.add(i);
				if (i * i != k) {
					pr.add(k / i);
				}
			}
		Collections.sort(pr);
		
		int l = 0, r = 0, x, y;
		long[] af = new long[n + 1];
		while (r < n) {
			while (l < n && a[l] == 0) l++;
			r = l;
			while (r < n && a[r] == 1) r++;
			x = r - l;
			l = r;

			y = 1;
			while (x > 0)
				af[x--] += y++;
		}

		l = 0; r = 0;
		long[] bf = new long[m + 1];
		while (r < m) {
			while (l < m && b[l] == 0) l++;
			r = l;
			while (r < m && b[r] == 1) r++;
			x = r - l;
			l = r;

			y = 1;
			while (x > 0)
				bf[x--] += y++;
		}

		ans = 0;
		int ptr = 0, sz = pr.size();
		while (ptr < sz) {
			x = pr.get(ptr);
			y = k / x;
			
			ptr++;
			if (x > n) continue;
			if (y > m) continue;
			ans += af[x] * bf[y];
		}
		out.println(ans);
		out.close();
	}

	
	
	int abs(int x) { if (x < 0) return -x; return x; }
	long abs(long x) { if (x < 0) return -x; return x; }
	int max(int x, int y) { if (x < y) return y; return x; }
	int min(int x, int y) { if (x > y) return y; return x; }
	long max(long x, long y) { if (x < y) return y; return x; }
	long min(long x, long y) { if (x > y) return y; return x; }
	int gcd(int x, int y) { while (y > 0) { x = y^(x^(y = x)); y %= x; } return x; }
	long gcd(long x, long y) { while (y > 0) { x = y^(x^(y = x)); y %= x; } return x; }
	long lcm(int x, int y) { return ((long) x) * (y / gcd(x, y)); }
	long lcm(long x, long y) { return x * (y / gcd(x, y)); }

	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine()); }
				catch (Exception e) {}
			} return st.nextToken();
		}
		int nextInt() { return Integer.parseInt(next()); }
		long nextLong() { return Long.parseLong(next()); }
		double nextDouble() { return Double.parseDouble(next()); }
	}
}
