#include <bits/stdc++.h>
using namespace std;
const int X = 100009;
int arr[X], Ans[X], n;
vector<int> V[X];
int T() {
  int MaX = 0;
  for (int i = 0; i < n; i++) {
    for (int l = 2; l * l <= arr[i]; l++)
      if (arr[i] % l == 0) {
        V[i].push_back(l);
        while (arr[i] % l == 0) arr[i] /= l;
      }
    if (arr[i] > 1) V[i].push_back(arr[i]);
  }
  for (int i = 0; i < n; i++) {
    int Res = 0;
    for (int q = 0; q < (int)V[i].size(); q++) Res = max(Ans[V[i][q]] + 1, Res);
    for (int q = 0; q < (int)V[i].size(); q++) Ans[V[i][q]] = Res;
    MaX = max(MaX, Res);
  }
  if (n == 1) return 1;
  return MaX;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  memset(Ans, 0, sizeof Ans);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  cout << T() << endl;
}

### Prompt

Please create a solution in CPP to the following problem:

Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a1, a2, ..., an are good.

Now she is interested in good sequences. A sequence x1, x2, ..., xk is called good if it satisfies the following three conditions:

  * The sequence is strictly increasing, i.e. xi < xi + 1 for each i (1 ≤ i ≤ k - 1). 
  * No two adjacent elements are coprime, i.e. gcd(xi, xi + 1) > 1 for each i (1 ≤ i ≤ k - 1) (where gcd(p, q) denotes the greatest common divisor of the integers p and q). 
  * All elements of the sequence are good integers. 



Find the length of the longest good sequence.

Input

The input consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 105) — the number of good integers. The second line contains a single-space separated list of good integers a1, a2, ..., an in strictly increasing order (1 ≤ ai ≤ 105; ai < ai + 1).

Output

Print a single integer — the length of the longest good sequence.

Examples

Input

5
2 3 4 6 9


Output

4


Input

9
1 2 3 5 6 7 8 9 10


Output

4

Note

In the first example, the following sequences are examples of good sequences: [2; 4; 6; 9], [2; 4; 6], [3; 9], [6]. The length of the longest good sequence is 4.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int X = 100009;
int arr[X], Ans[X], n;
vector<int> V[X];
int T() {
  int MaX = 0;
  for (int i = 0; i < n; i++) {
    for (int l = 2; l * l <= arr[i]; l++)
      if (arr[i] % l == 0) {
        V[i].push_back(l);
        while (arr[i] % l == 0) arr[i] /= l;
      }
    if (arr[i] > 1) V[i].push_back(arr[i]);
  }
  for (int i = 0; i < n; i++) {
    int Res = 0;
    for (int q = 0; q < (int)V[i].size(); q++) Res = max(Ans[V[i][q]] + 1, Res);
    for (int q = 0; q < (int)V[i].size(); q++) Ans[V[i][q]] = Res;
    MaX = max(MaX, Res);
  }
  if (n == 1) return 1;
  return MaX;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  memset(Ans, 0, sizeof Ans);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  cout << T() << endl;
}

```