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 Solution {
    public static void main(String[] args) {
//        BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
//        StringTokenizer st = new StringTokenizer(sc.readLine());
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();int m = sc.nextInt(); int k = sc.nextInt();

       int[] num1 = new int[n+1];
       int[] num2 = new int[m+1];

       int[] cnt1 = new int[n+2];
       int[] cnt2 = new int[m+2];

       for(int i=1;i<=n;i++){
           num1[i] = sc.nextInt();
           if(num1[i]!=0){
               num1[i]+=num1[i-1];
               cnt1[num1[i]]++;
           }
       }

       for(int i=n;i>=1;i--){
           cnt1[i] = cnt1[i] + cnt1[i+1];
       }


        for(int i=1;i<=m;i++){
            num2[i] = sc.nextInt();
            if(num2[i]!=0){
                num2[i]+=num2[i-1];
                cnt2[num2[i]]++;
            }
        }

        for(int i=m;i>=1;i--){
            cnt2[i] = cnt2[i] + cnt2[i+1];
        }

        long ans = 0L;
        for(int i=1;i<=n;i++){
            if(k%i!=0) continue;
            int j = k/i;
            if(j > m) continue;
            ans+= (cnt1[i]*cnt2[j]);
        }
        System.out.println(ans);
    }
}