#include <bits/stdc++.h>
using namespace std;
long long n, arr[100005], len[100005];
vector<long long> pf[100005];
void pre() {
  bool isp[100005];
  fill(isp, isp + 100005, true);
  isp[1] = false;
  for (long long i = 2; i < 100001; i++) {
    if (!isp[i]) continue;
    for (long long j = i; j < 100005; j += i)
      pf[j].push_back(i), isp[j] = false;
    isp[i] = true;
  }
}
void solve() {
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  long long ans = 0;
  pre();
  for (long long i = 0; i < n; i++) {
    long long temp = 0;
    for (auto x : pf[arr[i]]) temp = max(temp, len[x]);
    temp++;
    for (auto x : pf[arr[i]]) len[x] = temp;
    ans = max(ans, temp);
  }
  cout << ans << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  for (long long a = 0; a < t; a++) {
    solve();
  }
}

### Prompt

Generate a Cpp solution 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;
long long n, arr[100005], len[100005];
vector<long long> pf[100005];
void pre() {
  bool isp[100005];
  fill(isp, isp + 100005, true);
  isp[1] = false;
  for (long long i = 2; i < 100001; i++) {
    if (!isp[i]) continue;
    for (long long j = i; j < 100005; j += i)
      pf[j].push_back(i), isp[j] = false;
    isp[i] = true;
  }
}
void solve() {
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  long long ans = 0;
  pre();
  for (long long i = 0; i < n; i++) {
    long long temp = 0;
    for (auto x : pf[arr[i]]) temp = max(temp, len[x]);
    temp++;
    for (auto x : pf[arr[i]]) len[x] = temp;
    ans = max(ans, temp);
  }
  cout << ans << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  for (long long a = 0; a < t; a++) {
    solve();
  }
}

```