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.lang.*;

public class Main {

	public static void main(String[] args) {
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt(),m=in.nextInt(),k=in.nextInt();
		int[] a = new int[n];
		int[] b = new int[m];	
		int[] v1 = new int[n+1];
		int[] v2 = new int[m+1];
		for(int i=0;i<n;i++) {
			a[i] = in.nextInt();
		}
		for(int i=0;i<m;i++) {
			b[i] = in.nextInt();
		}
		for(int i=0;i<n;i++) {
			int t = 0;
			while(i<n && a[i]==1) { 
				i++;
				t++;
			}
			int temp = t;
			for(int j=1;j<=temp;j++) { 
				v1[j] += t;
				t--;
			}
		}
		for(int i=0;i<m;i++) {
			int t = 0;
			while(i<m && b[i]==1) {
				i++;
				t++;
			}
			int temp = t;
			for(int j=1;j<=temp;j++) {
				v2[j] += t;
				t--;
			}
		}
		long ans = 0;
		for(int i=1;i<=n;i++) {
			if(k%i==0 && (k/i)<=m)
				ans +=  v1[i]*v2[k/i];
		}	
		out.println(ans);
//		out.println(Arrays.toString(a));
//		out.println(Arrays.toString(b));
//		out.println(Arrays.toString(v1));
//		out.println(Arrays.toString(v2));		
		out.close();

	}

	static final Random random=new Random();
	static void ruffleSort(int[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n), temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	static void ruffleSort(char[] a) {
		int n=a.length;//shuffle, then sort 
		for (int i=0; i<n; i++) {
			int oi=random.nextInt(n);
			char temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	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; 
		} 

		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
	}
}













