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.lang.*;
import java.util.*;
public class Test
{
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int m=sc.nextInt();
        int k=sc.nextInt();
        int[] row=new int[n];
        int[] col=new int[m];
        for(int i=0;i<n;i++)
            row[i]=sc.nextInt();
        for(int i=0;i<m;i++)
            col[i]=sc.nextInt();
        Map<Integer,Integer> val=new HashMap<>();
        for(int i=1;i<=n;i++)
        {
            if (k % i == 0)
            {
                if(k/i<=m)
                    val.put(i, k / i);
            }
        }
        //System.out.println(val);
        long ans=0;
        for(int x : val.keySet())
        {
            int y=val.get(x);
            long count=0;
            int temp=0;
            for (int item : row)
            {
                if (item == 1)
                    temp++;
                else
                {
                    if (temp - x + 1 > 0)
                        count += (temp - x + 1);
                    temp = 0;
                }
            }
            if(temp-x+1>0)
                count+=(temp-x+1);
            int temp1=0;
            long count1=0;
            for (int value : col)
            {
                if (value == 1)
                    temp1++;
                else
                {
                    if (temp1 - y + 1 > 0)
                        count1 += (temp1 - y + 1);
                    temp1 = 0;
                }
            }
            if (temp1 - y + 1 > 0)
                count1 += (temp1 - y + 1);
            ans+=count*count1;
        }
        System.out.println(ans);
    }
}