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.Scanner;

public class Main{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
        int[] a=new int[n],b=new int[m];
        int[] conta=new int[n],contb=new int[m];
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
            if(i==0) conta[0]=a[0];
            else{
                if(a[i]==0){
                    conta[i]=0;
                }
                else{
                    conta[i]=conta[i-1]+1;
                }
            }
            
        }
        for(int i=0;i<m;i++){
            b[i]=sc.nextInt();
            if(i==0) contb[0]=b[0];
            else{
                if(b[i]==0){
                    contb[i]=0;
                }
                else{
                    contb[i]=contb[i-1]+1;
                }
            }
        }
        
        
        long count=0;
        for(int i=1;i<=Math.sqrt(k);i++){
            if(k%i==0){
                int fac1=i,fac2=k/i;
                int count1=0,count2=0;
                for(int j=0;j<n;j++){   //counting contigous fac1 1's in a 
                    if(conta[j]>=fac1) count1++;
                }
                for(int j=0;j<m;j++){   //counting contigous fac2 1's in b 
                    if(contb[j]>=fac2) count2++;
                }
                count+=(count1*count2);
                // System.out.println(fac1+" "+fac2+" "+count1+" "+count2);
                count1=count2=0;
                for(int j=0;j<n;j++){   //counting contigous fac2 1's in a 
                    if(conta[j]>=fac2) count1++;
                }
                for(int j=0;j<m;j++){   //counting contigous fac1 1's in b 
                    if(contb[j]>=fac1) count2++;
                }
                if(fac1==fac2)count1=count2=0;
                count+=(count1*count2);
                // System.out.println(fac1+" "+fac2+" "+count1+" "+count2);
            }
        }
        System.out.println(count);
    }
}