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.DataInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.List;
import java.util.stream.Collectors;

public class CFB {
    public static void main(String[] args) throws FileNotFoundException, InterruptedException {
        InputStream stream = System.in;
        Logger logger = new Logger();
        if (args.length>1 && args[0].equals("LOCAL") && args[1].equals("YES")) {
            File inputFile = new File("resources/input.in");
            stream = new DataInputStream(new FileInputStream(inputFile));
            logger.enableLogging(true, "resources/logs.txt");
        }
        InputReader in = new InputReader(stream);
        PrintWriter out = new PrintWriter(System.out);
        Thread th = new Thread(null, () -> new Task1().solve(in, out, logger), "Task1", 1 << 24);
        th.start();
        th.join();
        out.close();
        logger.close();
    }

    static class Task1 {
        void solve(InputReader in, PrintWriter out, Logger logger) {
            int n = in.nextInt(), m = in.nextInt(), k = in.nextInt(), a, b;
            ArrayList<Long> xGroup = new ArrayList<>();
            ArrayList<Long> yGroup = new ArrayList<>();

            long curr = 0;
            for(int i=0; i<n; i++) {
                a = in.nextInt();
                curr += a;
                if (a==0 && curr>0) {
                    xGroup.add(curr);
                    curr = 0;
                }

            }
            if (curr>0) {
                xGroup.add(curr);
                curr = 0;
            }
            for(int i=0; i<m; i++) {
                b = in.nextInt();
                curr += b;
                if(b==0 && curr>0) {
                    yGroup.add(curr);
                    curr = 0;
                }
            }
            if (curr>0) { yGroup.add(curr); }
            xGroup.forEach(element -> logger.log(element+" "));
            logger.logln("");
            yGroup.forEach(element -> logger.log(element+" "));
            logger.logln("");

            int kroot = (int)Math.sqrt(k);
            final long[] ans = {0};

            for (long ai=1; ai<=kroot; ai++) {
                long bj = k/ai;
                if (k == ai*bj) {
                    // find number of ai*bj matrices in yGroup[i]*xGroup[j]
                    long finalAi = ai, finalBj = bj;
                    List<Long> effectiveYGroup = yGroup.stream().filter(element -> element>=finalAi).collect(Collectors.toList());
                    List<Long> effectiveXGroup = xGroup.stream().filter(element -> element>=finalBj).collect(Collectors.toList());

                    if (effectiveXGroup.size()>0 && effectiveYGroup.size()>0){
                        long ySum = effectiveYGroup.stream().reduce(0L, Long::sum);
                        long xSum = effectiveXGroup.stream().reduce(0L, Long::sum);
                        ans[0] += (ySum - effectiveYGroup.size()*finalAi + effectiveYGroup.size())*(xSum - effectiveXGroup.size()*finalBj + effectiveXGroup.size());
                        logger.logln("xSum:"+xSum+" ySum:"+ySum+" "+ai+"*"+bj+": "+(ySum - effectiveYGroup.size()*finalAi + effectiveYGroup.size())*(xSum - effectiveXGroup.size()*finalBj + effectiveXGroup.size()));
                    }

                    if (ai != bj) {
                        // find number of bj*ai matrices in yGroup[i]*xGroup[j]
                        effectiveYGroup = yGroup.stream().filter(element -> element>=finalBj).collect(Collectors.toList());
                        effectiveXGroup = xGroup.stream().filter(element -> element>=finalAi).collect(Collectors.toList());
                        if (effectiveXGroup.size()>0 && effectiveYGroup.size()>0){
                            long ySum = effectiveYGroup.stream().reduce(0L, Long::sum);
                            long xSum = effectiveXGroup.stream().reduce(0L, Long::sum);
                            logger.logln("xSum:"+xSum+" ySum:"+ySum+" "+bj+"*"+ai+": "+(ySum - effectiveYGroup.size()*finalBj + effectiveYGroup.size())*(xSum - effectiveXGroup.size()*finalAi + effectiveXGroup.size()));
                            ans[0] += (ySum - effectiveYGroup.size()*finalBj + effectiveYGroup.size())*(xSum - effectiveXGroup.size()*finalAi + effectiveXGroup.size());
                        }
                    }
                    /*
                    for (int i=0; i<yGroup.size(); i++) {
                        for (int j=0; j<xGroup.size(); j++) {
                            if (yGroup.get(i) >= ai && xGroup.get(j) >= bj) {
                                ans[0] += (yGroup.get(i) - ai + 1)*(xGroup.get(j) - bj + 1);
                            }
                            if (yGroup.get(i) >= bj && xGroup.get(j) >= ai && ai != bj) {
                                ans[0] += (yGroup.get(i) - bj + 1)*(xGroup.get(j) - ai + 1);
                            }
                        }
                    }
                    */
                }
            }
            out.println(ans[0]);
        }
    }

    static class Logger {
        private PrintWriter logger;
        private boolean loggingEnabled;

        void enableLogging(boolean enable, String filename) {
            this.loggingEnabled = enable;
            try {
                if (loggingEnabled) this.logger = new PrintWriter(filename);
            } catch (FileNotFoundException ignored) {
            }
        }

        void log(Object s) {
            if (loggingEnabled) {
                logger.print(s.toString());
            }
        }

        void logln(Object s) {
            if (loggingEnabled) {
                logger.println(s.toString());
            }
        }

        void close() {
            if (loggingEnabled) logger.close();
        }
    }

    static class InputReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, numChars;
        private SpaceCharFilter filter;

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

        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++];
        }

        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;
        }

        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;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

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