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.*;
import java.io.*;
public class B6261
{
    public static void main(String [] args)
    {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt(); int m = sc.nextInt(); int k = sc.nextInt(); int [] a = new int [n];
        int [] b= new int [m];
        for (int i = 0; i < n; i++) a[i] = sc.nextInt();
        for (int i = 0; i < m; i++) b[i] = sc.nextInt();
        int run = 0; ArrayList<Integer> aRun = new ArrayList<>(); ArrayList<Integer> bRun = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (a[i] == 1) {
                run++;
            } else {
                aRun.add(run);
                run = 0;
            }
        }
        if (run > 0) aRun.add(run);
        run = 0;
        for (int i = 0; i < m; i++) {
            if (b[i] == 1) {
                run++;
            } else {
                bRun.add(run);
                run = 0;
            }
        }
        if (run > 0) bRun.add(run);
        Set<Integer> factors = new HashSet<>();
        for (int i = 1; i <= Math.sqrt(k); i++) {
            if (k % i == 0) {
                factors.add(i);
                factors.add(k / i);
            }
        }
        long ans = 0;
        for (Integer len: factors) {
            int other = k / len; long temp1 = 0; long temp2 = 0;
            for (Integer x: aRun) {
                if (x >= len) {
                    temp1 += (x - len + 1);
                }
            }
            for (Integer y: bRun) {
                if (y >= other) {
                    temp2 += (y - other + 1);
                }
            }
            ans += temp1 * temp2;
        }
        out.println(ans);
        out.close();
    }




    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }



    }

}