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.InputStreamReader;
import java.util.StringTokenizer;

public class CountSubRectangles {
    public static void main(String[] args) {
        FastReader input=new FastReader();
        int n,m,k;
        n=input.nextInt();
        m=input.nextInt();
        k=input.nextInt();
        int a[]=new int[n];
        int b[]=new int[m];
        int flag=0;
        int c=1;
        int p[]=new int[n+1];
        int max1=Integer.MIN_VALUE;
        for(int i=0;i<n;i++)
        {
            a[i]=input.nextInt();
            if(flag==0)
            {
                if(a[i]==1)
                {
                    flag=1;
                    c=1;
                }
            }
            else
            {
                if(a[i]==1)
                {
                    c++;
                }
                else
                {
                    p[c]++;
                    max1=Math.max(max1,c);
                    c=1;
                    flag=0;
                }
            }
        }
        if(a[n-1]==1)
        {
            max1=Math.max(max1,c);
            p[c]++;
        }
        flag=0;
        c=1;
        int max2=Integer.MIN_VALUE;
        int q[]=new int[m+1];
        for(int i=0;i<m;i++)
        {
            b[i]=input.nextInt();
            if(flag==0)
            {
                if(b[i]==1)
                {
                    flag=1;
                    c=1;
                }
            }
            else
            {
                if(b[i]==1)
                {
                    c++;
                }
                else
                {
                    q[c]++;
                    max2=Math.max(max2,c);
                    c=1;
                    flag=0;
                }
            }
        }
        if(b[m-1]==1)
        {
            max2=Math.max(max2,c);
            q[c]++;
        }
        long ans=0;
        for(int i=1;i<=Math.sqrt(k);i++)
        {
            if(k%i==0 && i!=k/i)
            {
                if(max1>=i && max2>=k/i)
                {
                    for(int j=i;j<=max1;j++)
                    {
                        if(p[j]>0)
                        {
                            for(int l=k/i;l<=max2;l++)
                            {
                                if(q[l]>0)
                                {
                                    ans+=(long)((j-i+1)*(l-k/i+1)*p[j]*q[l]);
                                }
                            }
                        }
                    }
                }
                if(max1>=k/i && max2>=i)
                {
                    for(int j=k/i;j<=max1;j++)
                    {
                        if(p[j]>0)
                        {
                            for(int l=i;l<=max2;l++)
                            {
                                if(q[l]>0)
                                {
                                    ans+=(long)((j-k/i+1)*(l-i+1)*p[j]*q[l]);
                                }
                            }
                        }
                    }
                }
            }
            else if(k%i==0 && i==k/i)
            {
                if(max1>=i && max2>=k/i)
                {
                    for(int j=i;j<=max1;j++)
                    {
                        if(p[j]>0)
                        {
                            for(int l=k/i;l<=max2;l++)
                            {
                                if(q[l]>0)
                                {
                                    ans+=(long)((j-i+1)*(l-k/i+1)*p[j]*q[l]);
                                }
                            }
                        }
                    }
                }
            }
        }
        System.out.println(ans);
    }
    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;
        }
    }
}
