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.io.*;
import java.util.*;
import java.text.*;
public final class isc
{
    static class FastReader 
    { 
 
        BufferedReader br; 
        StringTokenizer st; 
 
        public FastReader()
        { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
 
 
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
 
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
 
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
 
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
 
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }

    static int mindegree;
    static int[] finans;

    public static void main(String[] args)
    {
        FastReader sc = new FastReader();
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        int maken[] = new int[n];
        int makem[] = new int[m];
        int arrn[] = new int[n];
        int arrm[] = new int[m];
        for(int i=0; i<n; i++)
            arrn[i] = sc.nextInt();
        for(int i=0; i<m; i++)
            arrm[i] = sc.nextInt();
        maken = maker(arrn, n);
        makem = maker(arrm, m);
        long ans = 0;
        for(int i=1; i<=n; i++)
        {
            // i is edge of narr k/i is edge of marr
            if(k%i==0 && k/i<=m)
            {
                ans += 1l*maken[i]*makem[k/i];
            }
        }
        System.out.println(ans);
    }

    static int[] maker(int make[], int n)
    {
        int i = 0;
        int ans[] = new int[n+1];
        while(i<n)
        {
            if(make[i]==0)
            {
                i++;
                continue;
            }
            int j = i;
            while(j<n && make[j]!=0)
                j++;
            // System.out.println("I,J: "+i+" "+j);
            for(int len = 1; len<=j-i; len++)
                ans[len] += j-i-len+1;
            i=j;
        }
        // for(int j=0; j<=n; j++)
        //     System.out.print(ans[j]+" ");
        // System.out.println();
        return ans;
    }
}