#include <bits/stdc++.h>
using namespace std;
void file() {}
const long long nax = 1e5 + 1;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  file();
  int testCases = 1;
  while (testCases--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (long long i = 0; i < n; i++) {
      cin >> a[i];
    }
    vector<int> cnt(nax);
    int ans = 0;
    for (long long i = 0; i < n; i++) {
      int x = a[i];
      vector<int> div;
      div.push_back(x);
      for (long long i = 2; i <= sqrt(x); i++) {
        if (x % i == 0) {
          div.push_back(i);
          div.push_back(x / i);
        }
      }
      int maxi = 0;
      for (auto it : div) {
        maxi = max(maxi, cnt[it] + 1);
      }
      ans = max(ans, maxi);
      for (auto it : div) {
        cnt[it] = maxi;
      }
    }
    cout << ans;
  }
  return 0;
}

### 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;
void file() {}
const long long nax = 1e5 + 1;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  file();
  int testCases = 1;
  while (testCases--) {
    int n;
    cin >> n;
    vector<int> a(n);
    for (long long i = 0; i < n; i++) {
      cin >> a[i];
    }
    vector<int> cnt(nax);
    int ans = 0;
    for (long long i = 0; i < n; i++) {
      int x = a[i];
      vector<int> div;
      div.push_back(x);
      for (long long i = 2; i <= sqrt(x); i++) {
        if (x % i == 0) {
          div.push_back(i);
          div.push_back(x / i);
        }
      }
      int maxi = 0;
      for (auto it : div) {
        maxi = max(maxi, cnt[it] + 1);
      }
      ans = max(ans, maxi);
      for (auto it : div) {
        cnt[it] = maxi;
      }
    }
    cout << ans;
  }
  return 0;
}

```