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 {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static int[] a;
	static int[] b;
	static List<Integer> v = new ArrayList<>();
	static int n,m,k;
	
	
	public static void main(String[] args) throws Exception {
		st = new StringTokenizer(br.readLine());
		n = Integer.parseInt(st.nextToken());
		m = Integer.parseInt(st.nextToken());
		k = Integer.parseInt(st.nextToken());
		a = new int[n+1];
		b = new int[m+1];
		st = new StringTokenizer(br.readLine());
		for(int i=0; i<n; i++) {
			a[i] = Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(br.readLine());
		for(int i=0; i<m; i++) {
			b[i] = Integer.parseInt(st.nextToken());
		}
		int Max = Math.max(n, m);
		
		long ans = 0;
		for(int i=1; i<=Max; i++) {
			if(k%i==0) v.add(i); 
		}
		
		for(int i=0; i<v.size(); i++) {
			int num = v.get(i);
			int cnt = 0;
			int acnt = 0;
			for(int j=0; j < n; j++) {
				if(a[j]==1) {
					cnt++;
					if(j==n-1) {
						if(cnt>=num) {
							acnt += cnt-num+1;
						}	
					}
				}
				else if(a[j]==0) {
					if(cnt>=num) {
						acnt += cnt - num + 1;
					}
					cnt = 0;
				}
			}
			cnt = 0;
			int bcnt = 0;
			for(int j=0; j< m; j++ ) {
				if(b[j]==1) {
					cnt++;
					if(j==m-1) {
						if(cnt>=(k/num)) {
							bcnt += cnt-(k/num)+1;
						}
					}
				}
				else if(b[j]==0) {
					if(cnt>= (k/num)) {
						bcnt += cnt- (k/num) + 1;
					}
					cnt = 0;
				}
			}
			ans += acnt*bcnt;
		}
		System.out.println(ans);
	}
}
