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.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public final class Main
{
	static final long mod = 998244353l;

	public static void main(String[] args) throws IOException
	{
		Scanner in = getScan(args);
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		List<Integer> a = new ArrayList<>();
		int curr = 0;
		for (int i = 0; i < n; i++)
		{
			int c = in.nextInt();
			if (c == 0 && curr != 0)
			{
				a.add(curr);
				curr = 0;
			}
			if (c == 1)
			{
				curr++;
			}
		}
		if (curr != 0) a.add(curr);
		List<Integer> b = new ArrayList<>();
		curr = 0;
		for (int i = 0; i < m; i++)
		{
			int c = in.nextInt();
			if (c == 0 && curr != 0)
			{
				b.add(curr);
				curr = 0;
			}
			if (c == 1)
			{
				curr++;
			}
		}
		if (curr != 0) b.add(curr);
		List<Integer> kd = new ArrayList<>();
		for (int i = 1; i <= Math.sqrt(k); i++)
		{
			if (k % i == 0)
			{
				kd.add(i);
				kd.add(k / i);
			}
		}
		boolean sqr = k % Math.sqrt(k) == 0;
		int nbd = kd.size();
		long[] subseg_a = new long[nbd];
		long[] subseg_b = new long[nbd];
		int i = 0;
		for (int d : kd)
		{
			for (int ai : a)
			{
				subseg_a[i] += Math.max(0, ai - d + 1);
			}
			for (int bi : b)
			{
				subseg_b[i] += Math.max(0, bi - d + 1);
			}
			i++;
		}
		long nb = 0;
		for (i = 0; i < nbd - 2; i += 2)
		{
			nb += subseg_a[i] * subseg_b[i + 1];
			nb += subseg_a[i + 1] * subseg_b[i];
		}
		nb += subseg_a[i] * subseg_b[i + 1];
		if (!sqr)
		{
			nb += subseg_a[i + 1] * subseg_b[i];
		}
		System.out.println(nb);
	}

	public static long nb(int start, int a, int b, int k)
	{
		long res = 0;
		for (int i = start + 1; i <= Math.min(a, k); i++)
		{
			int r = k / i;
			if (k % i == 0 && b >= r)
			{
				res += Math.max(0, (b - r + 1) * (a - i + 1));
			}
		}
		return res;
	}

	public static long lcm(int number1, int number2)
	{
		if (number1 == 0 || number2 == 0)
		{
			return 0;
		}
		long absNumber1 = Math.abs(number1);
		long absNumber2 = Math.abs(number2);
		long absHigherNumber = Math.max(absNumber1, absNumber2);
		long absLowerNumber = Math.min(absNumber1, absNumber2);
		long lcm = absHigherNumber;
		while (lcm % absLowerNumber != 0)
		{
			lcm += absHigherNumber;
		}
		return lcm;
	}

	public static int log2nlz(int bits)
	{
		if (bits == 0) return 0; // or throw exception
		return 31 - Integer.numberOfLeadingZeros(bits);
	}

	static Scanner getScan(String[] args) throws IOException
	{
		if (args.length == 0)
		{
			return new Scanner(System.in);
		}
		else
		{
			return new Scanner(new File(args[0]));
		}
	}

}