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.*;
import java.io.*;

public class Main {

	public static void main(String[] args) throws Exception {
		int n=sc.nextInt();
		int m =sc.nextInt();
		int k=sc.nextInt();
		int[] a=new int[n];
		int[] b=new int[m];
		int c=0;
		for(int i=0;i<n;i++) {
			int z=sc.nextInt();
			if(z==0)
				c=0;
			else {
				c++;
			}
			if(c!=0) {
			a[c-1]++;
			}
		}
		c=0;
		for(int i=0;i<m;i++) {
			int z=sc.nextInt();
			if(z==0)
				c=0;
			else {
				c++;
			}
			if(c!=0) {
			b[c-1]++;
			}
		}
		for(int i=n-2;i>-1;i--) {
			a[i]+=a[i+1];
		}
		for(int i=m-2;i>-1;i--) {
			b[i]+=b[i+1];
		}

		long d=0;
		for(int i=0;i<n;i++) {
			if(k%(i+1)==0&&k/(i+1)<=m) {
				d+=a[i]*b[(k/(i+1))-1];
			}
		}
		pw.println(d);
		pw.close();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	static class pair implements Comparable<pair> {
		int x;
		int y;

		public pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public String toString() {
			return x + " " + y;
		}

		public int compareTo(pair other) {
			if (this.x == other.x) {
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}

	static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;

		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int compareTo(tuble other) {
			if (this.x == other.x) {
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		if (a == 0)
			return b;
		return (a > b) ? GCD(a % b, b) : GCD(a, b % a);
	}

	public static long LCM(long a, long b) {
		return a * b / GCD(a, b);
	}

	public static long nCk(int n, int k) { // O(K)
		if (k > n) {
			return 0;
		}
		long res = 1;
		for (int i = 1; i <= k; i++) {
			res = ((n - k + i) * res / i) % 1000000007;
		}
		return res;
	}

	public static long C(int a, int b, long[][] s) {
		int m = (int) 1e9 + 7;
		if (s[a][b] >= 0) {
			return s[a][b];
		} else if (a < b | a < 0 | b < 0) {
			s[a][b] = 0;
			return 0;
		} else if (a == b | b == 0) {
			s[a][b] = 1;
			return 1;
		} else {
			return s[a][b] = (C(a - 1, b, s) % m + C(a - 1, b - 1, s) % m) % m;
		}

	}

	public static boolean isprime(long a) {
		if (a == 0 || a == 1) {
			return false;
		}
		if (a == 2) {
			return true;
		}
		for (int i = 2; i < Math.sqrt(a) + 1; i++) {
			if (a % i == 0) {
				return false;
			}
		}
		return true;
	}

	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
}