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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Locale;
import java.util.Map.Entry;

import java.util.Random;
import java.util.Scanner;
import java.util.TreeSet;

public final class CF_626_D2_B {


	static boolean verb=true;
	static void log(Object X){if (verb) System.err.println(X);}
	static void log(Object[] X){if (verb) {for (Object U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X,int L){if (verb) {for (int i=0;i<L;i++) System.err.print(X[i]+" ");System.err.println("");}}
	static void log(long[] X){if (verb) {for (long U:X) System.err.print(U+" ");System.err.println("");}}

	static void logWln(Object X){if (verb) System.err.print(X);}
	static void info(Object o){	System.out.println(o);}
	static void output(Object o){outputWln(""+o+"\n");	}
	static void outputWln(Object o){try {out.write(""+ o);} catch (Exception e) {}}

	//static long mod=1000000007;
	static long mod=998244353 ; 
	static int CX=64;


	// Global vars
	static BufferedWriter out;
	static InputReader reader;

	static class Composite implements Comparable<Composite>{
		int v;
		int idx;

		public int compareTo(Composite X) {
			if (v!=X.v)
				return v-X.v;
			return idx-X.idx;
		}

		public Composite(int v, int idx) {
			this.v = v;
			this.idx = idx;
		}




	}


	static void process() throws Exception {

		Locale.setDefault(Locale.US);
		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader = new InputReader(System.in);


		int n=reader.readInt();
		int m=reader.readInt();
		int K=reader.readInt();

		TreeSet<Integer> ts=new TreeSet<Integer>();



		int cnt=0;
		int[] ha=new int[n+1];


		for (int i=0;i<n;i++) {
			int x=reader.readInt();
			//log("x:"+x);
			if (x==1) {
				cnt++;

			}
			if (x==0 || i==n-1) {
				//log("i:"+i);
				ha[cnt]++;
				cnt=0;
			}
		}

		cnt=0;

		int[] vb=new int[m+1];
		for (int i=0;i<m;i++) {
			int x=reader.readInt();
			if (x==1) {
				cnt++;

			}
			if (x==0 ||i==m-1) {
				vb[cnt]++;
				cnt=0;
			}
		}

		long res=0;

		//log(ha);
		//log(vb);

		for (int d=1;d*d<=K;d++) {
			if (K%d==0) {
				int x=d;
				int y=K/d;

				long tx,ty;
				tx=0;
				for (int u=x;u<=n;u++) {
					tx+=ha[u]*(1+u-x);
				}
				ty=0;
				for (int v=y;v<=m;v++) {
					ty+=vb[v]*(1+v-y);
				}
				res+=tx*ty;

				if (x!=y) {
					tx=0;
					ty=0;

					for (int u=y;u<=n;u++) {
						tx+=ha[u]*(1+u-y);
					}
					ty=0;
					for (int v=x;v<=m;v++) {
						ty+=vb[v]*(1+v-x);
					}
					res+=tx*ty;
				}
			}
		}
		output(res);


		try {
			out.close();
		} catch (Exception E) {
		}

	}

	public static void main(String[] args) throws Exception {
		process();

	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

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

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}

}