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 MyClass {
    
    public static void main(String args[]) {
      FastReader sc = new FastReader();     //For Fast IO
      int n = sc.nextInt();
      int m = sc.nextInt();      
      int k = sc.nextInt();
      HashMap<Long,Long> f1 = new HashMap<>();
      HashMap<Long,Long> f2 = new HashMap<>();
      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();
      }
      for(int i=0;i<n;i++){
          if(a[i]==1){
              long cnt=0;
              while(i<n && a[i]==1){
                  cnt++;
                  i++;
              }
              for(long j=1;j<=cnt;j++){
                  f1.put(j,f1.getOrDefault(j,0l)+cnt-j+1);
              }
          }
      }
      for(int i=0;i<m;i++){
          if(b[i]==1){
              long cnt=0;
              while(i<m && b[i]==1){
                  cnt++;
                  i++;
              }
              for(long j=1;j<=cnt;j++){
                  f2.put(j,f2.getOrDefault(j,0l)+cnt-j+1);
              }
          }
      }
      long ans=0;
      for(Long num : f1.keySet()){
          if(k%num == 0 && f2.get(k/num)!=null){
              ans += (f1.get(num)*f2.get(k/num));
          }
      }
      System.out.println(ans);
      
      
    }
}
class Pair{
    int x;
    int y;
    Pair(int i,int j){
        x=i;
        y=j;
    }
    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (!(o instanceof Pair)) return false;
        Pair key = (Pair) o;
        return x == key.x && y == key.y;
    }
    @Override
    public int hashCode() {
        int result = x;
        result = 31*result + y;
        return result;
    }
}
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; 
		} 
	}

	 	 
