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>
// package Div2_626;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class ProblemB {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String line[]=br.readLine().split(" ");
        int n=Integer.parseInt(line[0]);
        int m=Integer.parseInt(line[1]);
        long k=Long.parseLong(line[2]);
        HashSet<Long> factors=new HashSet<>();
        for(int i=1;i<=Math.sqrt(k);i++){
            if(k%i==0){
                long t=k/i;
                factors.add((long) i);
                factors.add(t);
            }
        }
        line=br.readLine().split(" ");
        int a[]=new int[n+1];
        int b[]=new int[m+1];
        for(int i=1;i<=n;i++){
            a[i]=Integer.parseInt(line[i-1]);
        }
        line=br.readLine().split(" ");
        for(int i=1;i<=m;i++){
            b[i]=Integer.parseInt(line[i-1]);
        }
        HashMap<Integer,Integer> columns=new HashMap<>();
        for(int i=1;i<=m;){
            int c=0;
            while(i<=m&&b[i]==1){
                i++;
                c++;
            }
            i++;
            columns.put(c,columns.getOrDefault(c,0)+1);
        }
        long ans=0;
        int row=0;
        for(int i=1;i<=n;){
//            System.out.println(ans);
            if(a[i]==1){
                row++;
                i++;
            }
            else{
                ans+=num(row,columns,factors,k);
                i++;
                row=0;
            }
        }
        if(row!=0){
            ans+=num(row,columns,factors,k);
        }
        System.out.println(ans);
//        System.out.println(factors.toString());
//        System.out.println(columns.toString());
    }
    public static long num(int m,HashMap<Integer,Integer> colums,HashSet<Long> fact,long k){
        long ans=0;
        for(long a:fact){
            for(int n:colums.keySet()){
                long b=k/a;
                int count=colums.get(n);
                if(m>=a&&n>=b){
                    ans+=1l*(m-a+1)*(n-b+1)*count;
                }
            }
        }
        return ans;
    }
}
