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.util.*;

public class CountSubrectangles {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int m = s.nextInt();
        int n = s.nextInt();
        int k = s.nextInt();
        long total = 0;
        int[] letX = new int[m];
        int[] letY = new int[n];
        ArrayList<Integer> recX = new ArrayList<Integer>();
        ArrayList<Integer> recY = new ArrayList<Integer>();
        int count = 0;
        for (int i = 0; i < m; i++) {
            int let = s.nextInt();
            letX[i] = let;
            if (let == 1) {
                count++;
            }
            else {
                recX.add(count);
                count = 0;
            }
        }
        if (count != 0) {
            recX.add(count);
            count = 0;
        }
        for (int i = 0; i < n; i++) {
            int let = s.nextInt();
            letY[i] = let;
            if (let == 1) {
                count++;
            }
            else {
                recY.add(count);
                count = 0;
            }
        }
        if (count != 0) {
            recY.add(count);
            count = 0;
        }
        ArrayList<Multiple> mults = getMult(k);
        for (int i = 0; i < mults.size(); i++) {
            Multiple a = mults.get(i);
            int xCount = 0;
            for (int j = 0; j < recX.size(); j++) {
                if (a.first <= recX.get(j)) {
                    xCount += recX.get(j) - a.first + 1;
                }
            }
            int yCount = 0;
            for (int j = 0; j < recY.size(); j++) {
                if (a.second <= recY.get(j)) {
                    yCount += recY.get(j) - a.second + 1;
                }
            }
            total += xCount * yCount;
        }
        System.out.println(total);
    }

    public static ArrayList<Multiple> getMult(int k) {
        ArrayList<Multiple> m = new ArrayList<Multiple>();
        for (int i = 1; i * i <= k; i++) {
            if (k % i == 0) {
                int val = k/i;
                m.add(new Multiple(i, val));
                if (val != i) {
                    m.add(new Multiple(val, i));
                }
            }
        }
        return m;
    }

    public static class Multiple {
        public int first;
        public int second;

        public Multiple(int first, int sec) {
            this.first = first;
            this.second = sec;
        }
    }
}
