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.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class ProblemB {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int m = scanner.nextInt();
			int k = scanner.nextInt();
			
			int[] nums1 = new int[n];
			int[] nums2 = new int[m];
			for (int i = 0; i < n; i++) {
				nums1[i] = scanner.nextInt();
			}
			for (int i = 0; i < m; i++) {
				nums2[i] = scanner.nextInt();
			}

			long[] count = {0};
			
			List<Integer> divs = printDivisors(k);
			Map<Integer, Integer> runs1 = findRuns(nums1);
			Map<Integer, Integer> runs2 = findRuns(nums2);
			runs1.forEach((s1, c1) -> {
				runs2.forEach((s2, c2) -> {
					for (Integer div : divs) {
						int div2 = k / div;
						
						if (s1 >= div && s2 >= div2) {
							count[0] += (s1 - div + 1) * c1 * (s2 - div2 + 1) * c2;
						}

						if (div != div2 && s1 >= div2 && s2 >= div) {
							count[0] += (s1 - div2 + 1) * c1 * (s2 - div + 1) * c2;
						}
					}
				});
			});
			System.out.println(count[0]);
		}
	}
	
	static List<Integer> printDivisors(int n) 
	{ 
		int max = (int) Math.sqrt(n);
		List<Integer> divs = new ArrayList<>();
	    for (int i=1;i<=max;i++) 
	        if (n%i==0) 
	            divs.add(i);
	    return divs;
	}
	
	static Map<Integer, Integer> findRuns(int[] nums) {
		Map<Integer, Integer> map = new HashMap<>();
		int runLength = -1;
		for (int i = 0; i < nums.length; i++) {
			if (nums[i] == 1) {
				runLength++;
			} else {
				if (runLength != -1) {
					Integer count = map.get(runLength + 1);
					if (count == null) {
						map.put(runLength + 1, 1);
					} else {
						map.put(runLength + 1, count + 1);
					}
					runLength = -1;
				}
			}
		}
		
		if (runLength != -1) {
			Integer count = map.get(runLength + 1);
			if (count == null) {
				map.put(runLength + 1, 1);
			} else {
				map.put(runLength + 1, count + 1);
			}
		}
		return map;
	}
}
