#include <bits/stdc++.h>
using namespace std;
int p[100004], prime[100004];
vector<int> v;
set<int> s;
int req[100004], ans[100004], a[100004];
int main() {
  ios_base::sync_with_stdio(0);
  int n, x, val, temp;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  if (n == 1) {
    cout << "1";
    return 0;
  }
  memset(req, 0, sizeof(req));
  for (int i = 0; i < n; i++) {
    int maxi = 0;
    v.clear();
    v.push_back(a[i]);
    for (int j = 2; j * j <= a[i]; j++) {
      if (a[i] % j == 0) {
        v.push_back(j);
        v.push_back(a[i] / j);
      }
    }
    for (int j = 0; j < v.size(); j++) maxi = max(maxi, req[v[j]]);
    for (int j = 0; j < v.size(); j++) req[v[j]] = maxi + 1;
    ans[i] = maxi + 1;
  }
  int ANS = -1;
  for (int i = 0; i < n; i++) ANS = max(ANS, ans[i]);
  cout << ANS;
}

### Prompt

Please formulate 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;
int p[100004], prime[100004];
vector<int> v;
set<int> s;
int req[100004], ans[100004], a[100004];
int main() {
  ios_base::sync_with_stdio(0);
  int n, x, val, temp;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  if (n == 1) {
    cout << "1";
    return 0;
  }
  memset(req, 0, sizeof(req));
  for (int i = 0; i < n; i++) {
    int maxi = 0;
    v.clear();
    v.push_back(a[i]);
    for (int j = 2; j * j <= a[i]; j++) {
      if (a[i] % j == 0) {
        v.push_back(j);
        v.push_back(a[i] / j);
      }
    }
    for (int j = 0; j < v.size(); j++) maxi = max(maxi, req[v[j]]);
    for (int j = 0; j < v.size(); j++) req[v[j]] = maxi + 1;
    ans[i] = maxi + 1;
  }
  int ANS = -1;
  for (int i = 0; i < n; i++) ANS = max(ANS, ans[i]);
  cout << ANS;
}

```