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>
//   package com.company;
  import java.util.*;
  import java.io.*;
  import java.lang.*;
  /*
  ** @author jigar_nainuji
   */
  public class Main{

      public static void main(String args[]){
          PrintWriter out=new PrintWriter(System.out);
          InputReader in=new InputReader(System.in);
          TASK solver = new TASK();
//          int t = in.nextInt();
          int t=1;
            for(int i=0;i<t;i++)
            {
                solver.solve(in,out,i);
            }
            out.close();
      }
      static class TASK{
          void solve(InputReader in,PrintWriter out,int testNumber) {
                  int n = in.nextInt();
                  int m = in.nextInt();
                  int k = in.nextInt();
                  int a[] = new int[n];
                  int b[] = new int[m];
                  int suffa[] = new int[n+1];
                  int suffb[] = new int[m+1];
                  for(int i=0;i<n;i++)
                      a[i]=in.nextInt();
                  for(int i=0;i<m;i++)
                      b[i]=in.nextInt();
                  int count=0;
                  for(int i=0;i<n;i++)
                  {
                      if(a[i]==0)
                      {
                          count=0;
                      }
                      else
                      {
                          count++;
                          suffa[count]++;
                      }
                  }
                  for(int i=n-1;i>=1;i--)
                      suffa[i]+=suffa[i+1];
                  count=0;
              for(int i=0;i<m;i++)
              {
                  if(b[i]==0)
                  {
                      count=0;
                  }
                  else
                  {
                      count++;
                      suffb[count]++;
                  }
              }
              for(int i=m-1;i>=1;i--)
                  suffb[i]+=suffb[i+1];
              long sum=0;
              for(int i=1;i<=n;i++)
              {
                  if(k%i==0 && k/i<=m)
                  {
                      sum+=suffa[i]*suffb[k/i];
                  }
                  if(i>k)
                      break;
              }
              System.out.println(sum);



          }
      }
      static class Maths{
          static long gcd(long a, long b) {
              if (a == 0)
                  return b;
              return gcd(b % a, a);
          }

          public  static long lcm(long a, long b)
          {
              return (a*b)/gcd(a, b);
          }

          public static long factorial(int n){
              long fact = 1;
              for(int i=1;i<=n;i++){
                  fact *= i;
              }
              return fact;
          }
      }
      static class InputReader {
          private InputStream stream;
          private byte[] buf = new byte[1024];
          private int curChar;
          private int numChars;
          private SpaceCharFilter filter;

          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() {
              BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
              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);
          }
      }
  }