#include <bits/stdc++.h>
using namespace std;
int val[100100];
int f[100100];
vector<int> pr;
vector<int> c;
int main() {
  int n;
  scanf("%d", &n);
  int gres = 0;
  for (int it = (0); it < (n); ++it) {
    int v;
    scanf("%d", &v);
    int nv = v;
    c.clear();
    int res = 0;
    for (int i = 2; i * i <= v; ++i) {
      if ((nv % i) == 0) {
        c.push_back(i);
        res = ((res < val[i]) ? (val[i]) : (res));
        while ((nv % i) == 0) nv /= i;
      }
    }
    if (nv > 1) {
      res = ((res < val[nv]) ? (val[nv]) : (res));
      c.push_back(nv);
    }
    for (int i = (0); i < (c.size()); ++i) val[c[i]] = res + 1;
    gres = ((gres < res + 1) ? (res + 1) : (gres));
  }
  cout << gres << endl;
  return 0;
}

### 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;
int val[100100];
int f[100100];
vector<int> pr;
vector<int> c;
int main() {
  int n;
  scanf("%d", &n);
  int gres = 0;
  for (int it = (0); it < (n); ++it) {
    int v;
    scanf("%d", &v);
    int nv = v;
    c.clear();
    int res = 0;
    for (int i = 2; i * i <= v; ++i) {
      if ((nv % i) == 0) {
        c.push_back(i);
        res = ((res < val[i]) ? (val[i]) : (res));
        while ((nv % i) == 0) nv /= i;
      }
    }
    if (nv > 1) {
      res = ((res < val[nv]) ? (val[nv]) : (res));
      c.push_back(nv);
    }
    for (int i = (0); i < (c.size()); ++i) val[c[i]] = res + 1;
    gres = ((gres < res + 1) ? (res + 1) : (gres));
  }
  cout << gres << endl;
  return 0;
}

```