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>
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
const int INF = 1e9;
const int MOD = 1e9 + 7;
long long c[N];
long long d[N];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m, k;
  cin >> n >> m >> k;
  long long cnt = 0;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    c[i] = x;
  }
  cnt = 0;
  for (int i = 0; i < m; i++) {
    int x;
    cin >> x;
    d[i] = x;
  }
  long long arr = 0;
  for (long long i = 1; i <= sqrt(k); i++) {
    long long cnt1 = 0, cnt2 = 0;
    cnt = 0;
    if (k % i == 0) {
      for (int j = 0; j < n; j++) {
        if (c[j] == 1)
          cnt++;
        else
          cnt = 0;
        if (cnt >= i) cnt1++;
      }
      cnt = 0;
      for (int j = 0; j < m; j++) {
        if (d[j] == 1)
          cnt++;
        else
          cnt = 0;
        if (cnt >= k / i) cnt2++;
      }
      arr += cnt1 * cnt2;
      cnt1 = cnt2 = cnt = 0;
      if (i != k / i) {
        for (int j = 0; j < m; j++) {
          if (d[j] == 1)
            cnt++;
          else
            cnt = 0;
          if (cnt >= i) cnt1++;
        }
        cnt = 0;
        for (int j = 0; j < n; j++) {
          if (c[j] == 1)
            cnt++;
          else
            cnt = 0;
          if (cnt >= k / i) cnt2++;
        }
        arr += cnt1 * cnt2;
      }
    }
  }
  cout << arr;
}
