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 {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<Long> arr = new ArrayList<>();
	
	static void gendivs(long x) {
		long i;
		for(i = 1; i * i < x; i++) {
			if(x % i == 0) {
				arr.add(i);
			}
		}
		
		if(i * i  == x) {
			arr.add(i);
		}
		
	}
	
	static long solve(int x, int y, long k) {
		long cur = 0;
		for(long div : arr) {
			long a = k/div, b = div;
			if(x >= a && y >= b) {
				cur += (x - a + 1) * (y - b + 1);
			}
			if(a != b && x >= b && y >= a) {
				cur += (x - b + 1) * (y - a + 1);
			}
		}
		return cur;
	}

	public static void main(String[] args) throws Exception {
		int n = sc.nextInt(), m = sc.nextInt();
		long k = sc.nextLong();
		TreeMap<Integer,Integer> a = new TreeMap<>();
		TreeMap<Integer,Integer> b = new TreeMap<>();
		gendivs(k);
		int cur = 0;
		for(int i = 0; i < n; i++) {
			int x = sc.nextInt();
			if(x == 1) cur++;
			else {
				a.put(cur, a.getOrDefault(cur,0) + 1);
				cur = 0;
			}
		}
		if(cur != 0) {
			a.put(cur,a.getOrDefault(cur,0) + 1);
			cur = 0;
		}
		
		for(int i = 0; i < m; i++) {
			int x = sc.nextInt();
			if(x == 1) cur++;
			else {
				b.put(cur,b.getOrDefault(cur, 0) + 1);
				cur = 0;
			}
		}
		
		if(cur != 0) {
			b.put(cur, b.getOrDefault(cur,0) + 1);
		}
		
		long ans = 0;
		for(Map.Entry<Integer,Integer> e : a.entrySet()) {
			for(Map.Entry<Integer,Integer> e2 : b.entrySet()) {
				long res = solve(e.getKey(),e2.getKey(), k);
				res *= e.getValue() * e2.getValue();
				ans += res;
			}
		}
		
		out.println(ans);
		out.close();
	}

}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public Scanner(String file) throws Exception {
		br = new BufferedReader(new FileReader(file));
	}

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

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

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

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