#include <bits/stdc++.h>
using namespace std;
int main() {
  const int MAX = 100000;
  int n;
  scanf("%d", &n);
  vector<bool> g(MAX + 1);
  for (int i = 0; i < n; i++) {
    int gi;
    scanf("%d", &gi);
    g[gi] = true;
  }
  vector<bool> sieve(MAX + 1);
  vector<vector<int>> pf(MAX + 1);
  for (int i = 2; i <= MAX; i++)
    if (!sieve[i])
      for (int j = i; j <= MAX; j += i) sieve[j] = true, pf[j].push_back(i);
  map<int, int> pl;
  for (int i = MAX; i >= 2; i--) {
    if (!g[i]) continue;
    int cmax = 0;
    for (int f : pf[i]) cmax = max(cmax, pl[f]);
    for (int f : pf[i]) pl[f] = cmax + 1;
  }
  int vmax = 1;
  for (auto &p : pl) vmax = max(vmax, p.second);
  printf("%d", vmax);
}

### 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 main() {
  const int MAX = 100000;
  int n;
  scanf("%d", &n);
  vector<bool> g(MAX + 1);
  for (int i = 0; i < n; i++) {
    int gi;
    scanf("%d", &gi);
    g[gi] = true;
  }
  vector<bool> sieve(MAX + 1);
  vector<vector<int>> pf(MAX + 1);
  for (int i = 2; i <= MAX; i++)
    if (!sieve[i])
      for (int j = i; j <= MAX; j += i) sieve[j] = true, pf[j].push_back(i);
  map<int, int> pl;
  for (int i = MAX; i >= 2; i--) {
    if (!g[i]) continue;
    int cmax = 0;
    for (int f : pf[i]) cmax = max(cmax, pl[f]);
    for (int f : pf[i]) pl[f] = cmax + 1;
  }
  int vmax = 1;
  for (auto &p : pl) vmax = max(vmax, p.second);
  printf("%d", vmax);
}

```