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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

import javax.sound.midi.Receiver;

/**
 * http://codeforces.com/contest/1323/problem/B
 */
public class TaskB {
    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int n = in.nextInt();
        final int m = in.nextInt();
        final int k = in.nextInt();
        final int[] a = in.readIntArr(n);
        final int[] b = in.readIntArr(m);
        int[] intervalsA = getIntervals(a);
        int[] intervalsB = getIntervals(b);
        long result = solution(intervalsA, intervalsB, k);
        out.printf("%d%n", result);
        out.close();
        in.close();
    }

    private static long solution(int[] intervalsA, int[] intervalsB, int k) {
        int[] div = divisors(k);
        long [][] divisors = new long[div.length][3];
        for(int i=0;i<divisors.length;i++){
            divisors[i][0]=div[i];
        }
        for(int i=0;i<divisors.length;i++){
            for(int j=0;j<intervalsA.length;j++){
                if(intervalsA[j]<divisors[i][0]){
                    continue;
                }
                divisors[i][1]+=intervalsA[j]-divisors[i][0]+1;
            }
            for(int j=0;j<intervalsB.length;j++){
                if(intervalsB[j]<k/divisors[i][0]){
                    continue;
                }
                divisors[i][2]+=intervalsB[j]-k/divisors[i][0]+1;
            }
        }

        long result =0;
        for(int i=0;i<divisors.length;i++){
            result+=divisors[i][1]*divisors[i][2];
        }
        return result;
    }


    private static int[] getIntervals(int[] a) {
        List<Integer> result = new ArrayList<Integer>();
        for (int i = 0; i < a.length; i++) {
            if (a[i] == 0) {
                continue;
            }
            int j = i;
            while (j < a.length && a[j] == 1) {
                j++;
            }
            result.add(j - i);
            i = j;
        }
        return result.stream().mapToInt(i -> i).toArray();
    }

    private static int[] divisors(final int k) {
        Set<Integer> result = new HashSet<>();
        for (int i = 1; i * i <= k; i++) {
            if (k % i == 0) {
                result.add(i);
                result.add(k / i);
            }
        }
        return result.stream().mapToInt(i -> i).toArray();
    }

    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

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

    }

}