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 B implements Runnable
{
    @Override
    public void run() {
        InputReader in = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int m = in.nextInt();
        int n = in.nextInt();
        int k = in.nextInt();
        int[] a1 = new int[m];
        int[] a2 = new int[n];
        for (int i = 0; i < m; i++) {
            a1[i] = in.nextInt();
        }
        for (int i = 0; i < n; i++) {
            a2[i] = in.nextInt();
        }
        getRes(a1, a2, k, w);
        w.flush();
        w.close();
    }

    private static void getRes(int[] a1, int[] a2, int k, PrintWriter w) {
        int[] m1 = getMap(a1);
        int[] m2 = getMap(a2);
        long res = 0;
        
        int[] c1 = new int[a1.length + 1];
        int[] larger1 = new int[a1.length + 1];
        larger1[a1.length] = m1[a1.length] * a1.length;
        c1[a1.length] = m1[a1.length];
        for (int i = a1.length - 1; i > 0; i--) {
            larger1[i] = larger1[i + 1] + m1[i] * i;
            c1[i] = c1[i + 1] + m1[i];
        }
        int[] c2 = new int[a2.length + 1];
        int[] larger2 = new int[a2.length + 1];
        larger2[a2.length] = m2[a2.length] * a2.length;
        c2[a2.length] = m2[a2.length];
        for (int i = a2.length - 1; i > 0; i--) {
            larger2[i] = larger2[i + 1] + m2[i] * i;
            c2[i] = c2[i + 1] + m2[i];
        }

        for (int i = 1; i * i <= k; i++) {
            // if (i == 1) {
            //     System.out.println(c1[1] + " " + larger1[1] + " " + c2[1] + " " + + larger2[1]);
            // }
            if (k % i == 0) {
                int d = k / i;
                if (i <= a1.length && d <= a2.length && c1[i] != 0 && c2[d] != 0) {
                    res += (larger1[i] - (c1[i]) * (i - 1)) * (larger2[d] - (c2[d]) * (d - 1));
                    //System.out.println(i + " " + res);
                }
                if (i == d) {
                    break;
                }
                if (i <= a2.length && d <= a1.length && c2[i] != 0 && c1[d] != 0) {
                    res += (larger2[i] - (c2[i]) * (i - 1)) * (larger1[d] - (c1[d]) * (d - 1));
                    //System.out.println(i + " " + res);
                }
            }
        }
        w.println(res);
    }

    private static int[] getMap(int[] a) {
        int[] map = new int[a.length + 1];
        int count = 0;
        for (int num : a) {
            if (num == 1) {
                count++;
            }
            else {
                if (count != 0) {
                    map[count]++;
                }
                count = 0;
            }
        }
        if (count != 0) {
            map[count]++;
        }
        // for (int i = 0; i <= a.length; i++) {
        //     System.out.print(map[i] + " ");
        // }
        //System.out.println();
        return map;
    }
    static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-')
            {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do
            {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception
    {
        new Thread(null, new B(),"Main",1<<27).start();
    }

}
