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.*;

public class cf1323_Div2_B {
	
	public static int[] segments(int[] arr) {
		int n = arr.length;
		int[] seg = new int[n + 1];
		for (int i = 0; i < n; ) {
			if (arr[i] == 0) {
				i++;
				continue;
			}
			
			int j = i;
			while (j < n && arr[j] == 1) {
				j++;
			}
			
			for (int len = 1; len < (j - i) + 1; len++) {
				seg[len] += j - i - len + 1;
			}
			
			i = j;
		}
		
		return seg;
	}
		
	public static void main(String[] args) throws IOException {
       FastScanner in = new FastScanner();
       int n = in.nextInt();
       int m = in.nextInt();
       int k = in.nextInt();
       long total = 0;
       int[] row = new int[n];
       for (int i = 0; i < n; i++)
    	   row[i] = in.nextInt();
       int[] col = new int[m];
       for (int i = 0; i < m; i++)
    	   col[i] = in.nextInt();
       
       // count total number of 1 as if the entire grid is just filled with ones of sub of size k
       
       int[] seg1 = segments(row);
       int[] seg2 = segments(col);
       // System.out.println(Arrays.toString(seg1));
       // System.out.println(Arrays.toString(seg2));
       long t = 0;
       for (int i = 1; i * i <= k; i++) {
    	   if (k % i == 0) {
    		   if (i < seg1.length && k / i < seg2.length)
    			   t += seg1[i] * seg2[k / i];
    		   if (i < seg2.length && k / i < seg1.length && i != k / i)
    			   t += seg2[i] * seg1[k / i];
    	   }
       }
       total = t;
       System.out.println(total);
       
    }
    
    public static void shuffle(int[] arr) {
    	Random rgen = new Random();
    	
    	for (int i = 0; i < arr.length; i++) {
    		int rPos = rgen.nextInt(arr.length);
    		int temp = arr[i];
    		arr[i] = arr[rPos];
    		arr[rPos]=temp;
    	}
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

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

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

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}

