#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, i;
  cin >> n;
  vector<int> v(n);
  for (i = 0; i < n; i++) {
    cin >> v[i];
  }
  vector<int> factorise(v);
  vector<vector<int> > previous(n);
  for (i = 2; i < 317; i++) {
    int prev = -1;
    for (int j = 0; j < n; j++) {
      if (v[j] % i == 0) {
        while (factorise[j] % i == 0) factorise[j] /= i;
        if (prev != -1) previous[j].push_back(prev);
        prev = j;
      }
    }
  }
  map<int, int> m;
  for (i = 0; i < n; i++) {
    if (factorise[i] == 1) continue;
    if (m.count(factorise[i]) == 1) {
      previous[i].push_back(m[factorise[i]]);
    }
    m[factorise[i]] = i;
  }
  vector<int> dp(n);
  for (i = 0; i < n; i++) {
    int maxx = 1;
    for (int j = 0; j < previous[i].size(); j++) {
      int k = dp[previous[i][j]];
      if (k + 1 > maxx) maxx = k + 1;
    }
    dp[i] = maxx;
  }
  int allmax = 0;
  for (i = 0; i < n; i++) {
    if (dp[i] > allmax) allmax = dp[i];
  }
  cout << allmax;
}

### 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;
int main() {
  int n, i;
  cin >> n;
  vector<int> v(n);
  for (i = 0; i < n; i++) {
    cin >> v[i];
  }
  vector<int> factorise(v);
  vector<vector<int> > previous(n);
  for (i = 2; i < 317; i++) {
    int prev = -1;
    for (int j = 0; j < n; j++) {
      if (v[j] % i == 0) {
        while (factorise[j] % i == 0) factorise[j] /= i;
        if (prev != -1) previous[j].push_back(prev);
        prev = j;
      }
    }
  }
  map<int, int> m;
  for (i = 0; i < n; i++) {
    if (factorise[i] == 1) continue;
    if (m.count(factorise[i]) == 1) {
      previous[i].push_back(m[factorise[i]]);
    }
    m[factorise[i]] = i;
  }
  vector<int> dp(n);
  for (i = 0; i < n; i++) {
    int maxx = 1;
    for (int j = 0; j < previous[i].size(); j++) {
      int k = dp[previous[i][j]];
      if (k + 1 > maxx) maxx = k + 1;
    }
    dp[i] = maxx;
  }
  int allmax = 0;
  for (i = 0; i < n; i++) {
    if (dp[i] > allmax) allmax = dp[i];
  }
  cout << allmax;
}

```