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 {

	public static void main(String[] args) throws Exception {
		
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		
		StringTokenizer st = new StringTokenizer(in.readLine());
		
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		long k = Integer.parseInt(st.nextToken());
		
		int[] a = new int[n];
		int[] b = new int[m];
		
		st = new StringTokenizer(in.readLine());
		ArrayList<Integer> aones = new ArrayList<Integer>();
		
		int count = 0;
		for(int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(st.nextToken());
			if(a[i] == 1) count++;
			else {
				if(count > 0) aones.add(count);
				count = 0;
			}
		}
		
		if(count > 0) aones.add(count);
		
		st = new StringTokenizer(in.readLine());
		ArrayList<Integer> bones = new ArrayList<Integer>();
		
		count = 0;
		for(int i = 0; i < m; i++) {
			b[i] = Integer.parseInt(st.nextToken());
			if(b[i] == 1) count++;
			else {
				if(count > 0) bones.add(count);
				count = 0;
			}
		}
		
		if(count > 0) bones.add(count);
		
		ArrayList<Long> fact = new ArrayList<Long>();
		
		for(long i = 1; i*i <= k; i++) {
			if(k % i == 0) {
				fact.add(i);
				if(i != k/i)
				fact.add(k/i);
			}
		}
		
//		System.out.println(aones);
//		System.out.println(bones);
		
		long tot = 0;
		for(long f: fact) {
			
			int itot = 0;
			for(int x: aones) {
				if(x-f+1 > 0) itot += x-f+1;
			}
			
			long f2 = k/f;
			int jtot = 0;
			for(int x: bones) {
				if(x-f2+1 > 0) jtot += x-f2+1;
			}
			
			tot += (long) itot * jtot;
//			System.out.println(tot + " " + f + " " + itot + " " + jtot);
		}
		
		System.out.println(tot);
	}
}
