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.*;

//solution classes here

public class Code {

    //main solution here

    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        int a[] = new int[n+1];
        int b[] = new int[m+1];
        for(int i=1;i<=n;i++) {
            a[i] = sc.nextInt();
            a[i]+=a[i-1];
        }
        for(int i=1;i<=m;i++) {
            b[i] = sc.nextInt();
            b[i]+=b[i-1];
        }


        ArrayList<Integer> l1 = new ArrayList<>();
        ArrayList<Integer> l2 = new ArrayList<>();
        for(int i=1;i*i<=k;i++) {
            if(k%i==0) {
                if(i==k/i) {
                    if(i<=n && k/i<=m) {
                        l1.add(i);
                        l2.add(k/i);
                    }
                }
                else {
                    if (i <= n && k / i <= m) {
                        l1.add(i);
                        l2.add(k / i);
                    }
                    if (i <= m && k / i <= n) {
                        l2.add(i);
                        l1.add(k / i);
                    }
                }
            }
        }

        int len = l1.size();
        long total=0;
        for(int i=0;i<len;i++) {
            long c1=0;
            long c2=0;
            int v1 = l1.get(i);
            int v2 = l2.get(i);
            for(int j=v1;j<=n;j++) {
                if(a[j]-a[j-v1]==v1) {
                    c1++;
                }
            }
            for(int j=v2;j<=m;j++) {
                if(b[j]-b[j-v2]==v2) {
                    c2++;
                }
            }
            total+=c1*c2;
        }
        out.println(total);

        out.flush();
        out.close();
    }

    //solution functions here


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}

/* *****************************************************************************************************************************
 * I'M NOT IN DANGER, I'M THE DANGER!!!
 *
 *  94 40 49 65 21 21 106 80 92 81 679 4 61
  6 237 12 72 74 29 95 265 35 47 1 61 397
  52 72 37 51 1 81 45 435 7 36 57 86 81 72
 * *****************************************************************************************************************************
 */