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.Arrays;
import java.util.Scanner;
public class paran
{
	public static void main (String[] args)
	 {
		Scanner sc=new Scanner(System.in); 
		int t,i;
		t=1;
		while(t>0)
		{
			t--;
			int n=sc.nextInt();
			int m=sc.nextInt();
			int k=sc.nextInt();
			int c[]=new int[n];
			int r[]=new int[m];
			for(i=0;i<n;i++)
				c[i]=sc.nextInt();
			for(i=0;i<m;i++)
				r[i]=sc.nextInt();
			int f[]=new int[(int)Math.sqrt(k)+1];
			getD(k,f);
			long ans=0;
			for(i=0;i<f.length;i++)
			{
				if(f[i]==1)
				{
					ans+=calc(i,k/i,n,m,r,c);
					if(i!=k/i)
					ans+=calc(k/i,i,n,m,r,c);
				}
			}
			System.out.println(ans);
		}
	}
	static void getD(int n,int f[]) 
    { 
        for (int i=1; i<=Math.sqrt(n); i++) 
        { 
            if (n%i==0) 
            	f[i]=1;
        } 
    } 
	static long calc(int row,int col,int n,int m,int r[],int c[])
	{
		int i;
		int l=0;
		int h=0;
		int t=0;
		for(i=0;i<n;i++)
		{
			if(c[i]==1)
			{
				t++;
				if(t>=col)
					l++;
			}
			else
				t=0;
		}
		t=0;
		for(i=0;i<m;i++)
		{
			if(r[i]==1)
			{
				t++;
				if(t>=row)
					h++;
			}
			else
				t=0;
		}
		return (long)l*h;
	}
}