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.*;
public class subrectangles {
	public static void main(String[] args) {
		
		Scanner x = new Scanner(System.in);
		int n = x.nextInt();
		int m = x.nextInt();
		int k = x.nextInt();
		int[] narr = new int[n];
		int[] marr = new int[m];
		for(int i = 0; i < n; i++) {
			narr[i] = x.nextInt();
		}
		for(int i = 0; i < m; i++) {
			marr[i]= x.nextInt();
		}
		ArrayList<Integer> continuousm = new ArrayList<Integer>();
		ArrayList<Integer> continuousn = new ArrayList<Integer>();
		ArrayList<Integer> preN = new ArrayList<Integer>();

		ArrayList<Integer> preM = new ArrayList<Integer>();


		int sum = 0;
		for(int i = 0; i < m; i++) {
			if (marr[i] == 1) {
				sum += 1;
			}else {
				if (sum != 0) {
					continuousm.add(sum);
					sum = 0;
				}
			}
		}
		if (sum != 0) {
			continuousm.add(sum);
			sum = 0;
		}
		sum = 0;
		for(int i = 0; i < n; i++) {
			if (narr[i] == 1) {
				sum += 1;
			}else {
				if (sum != 0) {
					continuousn.add(sum);
					sum = 0;
				}
			}
		}
		if (sum != 0) {
			continuousn.add(sum);
			sum = 0;
		}
		sum = 0;
		Collections.sort(continuousn);
		Collections.sort(continuousm);
		preN.add(0);
		preM.add(0);
		for(int i = 0; i < continuousn.size(); i++) {
			sum += continuousn.get(i);
			preN.add(sum);
		}
		sum = 0;
		for(int i = 0; i < continuousm.size(); i++) {
			sum += continuousm.get(i);
			preM.add(sum);
		}
		long totalSum = 0;
		for(int i = 1; i < (int)(Math.sqrt(k)) + 1; i++) {
			if (k % i == 0) {
				int first = i;
				int second = k / i;
				int firstM = 0;
				int secondM = 0;
				int firstIndex = binarySearch(first, continuousm, 0, continuousm.size()/2, continuousm.size()-1);
				int secondIndex = binarySearch(second, continuousm, 0, continuousm.size()/2, continuousm.size()-1);
				long firstSum = preM.get(preM.size() - 1) - preM.get(firstIndex) - (first-1) * (preM.size() - firstIndex - 1);
				long secondSum = preM.get(preM.size() - 1) - preM.get(secondIndex) - (second-1) * (preM.size() - secondIndex - 1);
				int thirdIndex = binarySearch(first, continuousn, 0, continuousn.size()/2, continuousn.size()-1);
				int fourthIndex = binarySearch(second, continuousn, 0, continuousn.size()/2, continuousn.size()-1);
				long thirdSum = preN.get(preN.size() - 1) - preN.get(thirdIndex) - (first-1) * (preN.size()- thirdIndex - 1);
				long fourthSum = preN.get(preN.size() - 1) - preN.get(fourthIndex) - (second-1) * (preN.size() - fourthIndex - 1);
				if (first != second)totalSum += firstSum * fourthSum + secondSum * thirdSum;
				else totalSum += firstSum * fourthSum;
			}
		}
		System.out.println(totalSum);
	}
	
	public static int binarySearch(int num, ArrayList<Integer> list, int low, int medium, int high) {
		if (low > high) {
			return low;
		}
		else if(num > list.get(medium)) {
			return binarySearch(num, list, medium + 1, (low + high) / 2, high);
		}
		else {
			return binarySearch(num, list, low, (low + high)/2, medium - 1);
		}
	}
}
