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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class A {

	public static void main(String[] args) throws NumberFormatException, IOException
	{
		new A().run();
	}
	
	public void run() throws NumberFormatException, IOException {
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(file.readLine());
		int N = Integer.parseInt(st.nextToken());
		int M = Integer.parseInt(st.nextToken());
		int K = Integer.parseInt(st.nextToken());
		ArrayList<Integer> factors = new ArrayList<Integer>();//be careful of SR
		int sqrt = (int)(Math.sqrt(K));
		for(int i = 1;i<=sqrt;i++)
		{
			if(K%i == 0)
			{
				factors.add(i);
				if(i*i != K)
					factors.add(K/i);
			}
		}
		int[] rowa = new int[N];
		int[] rowb = new int[M];
		int[] a = new int[N];
		int[] b = new int[M];
		st = new StringTokenizer(file.readLine());
		for(int i = 0;i<N;i++)
		{
			a[i] = Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(file.readLine());
		for(int i = 0;i<M;i++)
		{
			b[i] = Integer.parseInt(st.nextToken());
		}
		rowa[0] = a[0];
		rowb[0] = b[0];
		for(int i = 1;i<rowa.length;i++)
		{
			if(a[i] == 1)
				rowa[i] = rowa[i-1]+1;
		}
		for(int i = 1;i<rowb.length;i++)
		{
			if(b[i] == 1)
				rowb[i] = rowb[i-1]+1;
		}
		long ans = 0;
		for(int i = 0;i<factors.size();i++)
		{
			int facta = factors.get(i);
			int factb = K/facta;
			int xx = 0;
			int yy = 0;
			for(int j = 0;j<rowa.length;j++)
			{
				if(rowa[j] >= facta)
					xx++;
			}
			for(int j = 0;j<rowb.length;j++)
			{
				if(rowb[j] >= factb)
					yy++;
			}
			ans += xx*yy;
		}
		System.out.println(ans);
		//SUBTRACT OUT SR
	}
	
}
