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 Cf20{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int[] mnk = Arrays.asList(sc.nextLine().split(" ")).stream().mapToInt(Integer::parseInt).toArray();
        int[] col = Arrays.asList(sc.nextLine().split(" ")).stream().mapToInt(Integer::parseInt).toArray();
        int[] row = Arrays.asList(sc.nextLine().split(" ")).stream().mapToInt(Integer::parseInt).toArray();
        Map<Integer, Integer> cmap = new HashMap<>();
        Map<Integer, Integer> rmap = new HashMap<>();
        for(int i=0;i<mnk[0];i++){
            if(col[i]==0) {
                col[i] = i==0?col[i]:col[i]+col[i - 1];
                cmap.put(col[i],cmap.getOrDefault(col[i],0)+1);
                col[i] = 0;
            }
            else
                col[i] = i==0?col[i]:col[i]+col[i - 1];
            if(col[i]!=0&&i==mnk[0]-1)
                cmap.put(col[i],cmap.getOrDefault(col[i],0)+1);
        }
        for(int i=0;i<mnk[1];i++){

            if(row[i]==0) {
                row[i] = i==0?row[i]:row[i]+row[i - 1];
                rmap.put(row[i],rmap.getOrDefault(row[i],0)+1);
                row[i] =0;
            }
            else
                row[i] = i==0?row[i]:row[i]+row[i - 1];
            if(row[i]!=0&&i==mnk[1]-1)
                rmap.put(row[i],rmap.getOrDefault(row[i],0)+1);
        }
        long ans =0;
        for(int i=1;i<=mnk[2];i++){
            if(i>mnk[0])
                break;
            if(mnk[2]%i!=0)
                continue;
            int c = 0;
            for(int key:cmap.keySet()){
                if(key<i)
                    continue;
                int temp = key-i+1;
                temp *= cmap.get(key);
                c += temp;
            }
            int r = 0;
            for(int key:rmap.keySet()){
                if(key<mnk[2]/i)
                    continue;
                int temp = key-mnk[2]/i+1;
                temp *= rmap.get(key);
                r += temp;
            }
            ans += r*c;
        }
        System.out.println(ans);

    }


}