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.Scanner;
public class Main {
	static ArrayList<Integer> cona = new ArrayList<>();
	static ArrayList<Integer> conb = new ArrayList<>();
    public static void main(String[] args) {
	    Scanner s = new Scanner(System.in);
	    int n = s.nextInt();
	    int m  = s.nextInt();
	    int k = s.nextInt();
	    int[] a = new int[n];
	    int[] b = new int[m];
		for(int i=0;i<n;i++){
	        a[i] = s.nextInt();
        }
	    for(int i=0;i<m;i++){
	        b[i] = s.nextInt();
        }
	    int count =0;
	    for(int i=0;i<n;i++){
	    	if(a[i]==1){
	    		count++;
			}
	    	else{
	    		cona.add(count);
	    		count =0;
			}
		}
	    cona.add(count);
	    count =0;
	    for(int i =0;i<m;i++){
	    	if(b[i]==1){
	    		count++;
			}
	    	else{
	    		conb.add(count);
	    		count =0;
			}
		}
	    long ans = 0;
	    conb.add(count);
	    int p =0;
	    for(int i=1;i<(int)(Math.sqrt(k)+1);i++){
	    	if(k%i==0) {
				p = k / i;
				ans += answer(p, i, cona, conb);

				if (i != p) {
					ans += answer(i , p, cona, conb);
				}
			}
		}
		System.out.println(ans);

    }
    public static long answer(int p,int q,ArrayList<Integer> u,ArrayList<Integer> v){
    	int m =0;
    	int nm =0;
    	for(int i=0;i<cona.size();i++) {
			m += Math.max(cona.get(i)-(p-1),0);
		}
    	for(int i=0;i<conb.size();i++){
    		nm += Math.max(conb.get(i)-(q-1),0);
		}
    	return nm*m;
	}
}
