#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const int N = 100010;
int a[N];
vector<int> f[N];
void go() {
  long long n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 2; i < N; i++) {
    for (int j = i; j < N; j += i) f[j].push_back(i);
  }
  int freq[N] = {0};
  for (int i = 0; i < n; i++) {
    int m = 0;
    for (auto x : f[a[i]]) {
      m = max(m, freq[x] + 1);
    }
    freq[a[i]] = m;
    for (auto x : f[a[i]]) {
      freq[x] = m;
    }
  }
  int ans = 1;
  for (int i = 0; i < n; i++) {
    ans = max(freq[a[i]], ans);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t = 1;
  cout << fixed << setprecision(9);
  while (t--) {
    go();
  }
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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 long long MOD = 1e9 + 7;
const int N = 100010;
int a[N];
vector<int> f[N];
void go() {
  long long n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 2; i < N; i++) {
    for (int j = i; j < N; j += i) f[j].push_back(i);
  }
  int freq[N] = {0};
  for (int i = 0; i < n; i++) {
    int m = 0;
    for (auto x : f[a[i]]) {
      m = max(m, freq[x] + 1);
    }
    freq[a[i]] = m;
    for (auto x : f[a[i]]) {
      freq[x] = m;
    }
  }
  int ans = 1;
  for (int i = 0; i < n; i++) {
    ans = max(freq[a[i]], ans);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  int t = 1;
  cout << fixed << setprecision(9);
  while (t--) {
    go();
  }
}

```