#include <bits/stdc++.h>
using namespace std;
const int M = (int)(2e6 + 239);
int a[(int)(1e5 + 7)], ans[(int)(1e5 + 7)];
void rll(int x) {
  int z = x;
  vector<int> nn;
  int sol = 0;
  for (int i = 2; i <= (int)sqrt(x); i++) {
    if (z % i == 0) {
      while (z % i == 0) {
        z /= i;
      }
      nn.push_back(i);
      ans[i]++;
      sol = max(sol, ans[i]);
    }
  }
  if (z > 1) {
    ans[z]++;
    nn.push_back(z);
    sol = max(sol, ans[z]);
  }
  for (int i = 0; i < (int)nn.size(); i++) {
    ans[nn[i]] = sol;
  }
  return;
}
void solve() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    rll(a[i]);
  }
  int sz = 1;
  for (int i = 0; i < (int)(1e5 + 7); i++) {
    sz = max(sz, ans[i]);
  }
  cout << sz << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  solve();
  return 0;
}

### Prompt

Create a solution in Cpp for 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 M = (int)(2e6 + 239);
int a[(int)(1e5 + 7)], ans[(int)(1e5 + 7)];
void rll(int x) {
  int z = x;
  vector<int> nn;
  int sol = 0;
  for (int i = 2; i <= (int)sqrt(x); i++) {
    if (z % i == 0) {
      while (z % i == 0) {
        z /= i;
      }
      nn.push_back(i);
      ans[i]++;
      sol = max(sol, ans[i]);
    }
  }
  if (z > 1) {
    ans[z]++;
    nn.push_back(z);
    sol = max(sol, ans[z]);
  }
  for (int i = 0; i < (int)nn.size(); i++) {
    ans[nn[i]] = sol;
  }
  return;
}
void solve() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    rll(a[i]);
  }
  int sz = 1;
  for (int i = 0; i < (int)(1e5 + 7); i++) {
    sz = max(sz, ans[i]);
  }
  cout << sz << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  solve();
  return 0;
}

```