#include <bits/stdc++.h>
using namespace std;
int n;
int pos[100010];
int mem[100010];
bool pr[100010];
vector<int> adj[100010];
int main() {
  memset(pos, -1, sizeof pos);
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    pos[a] = i;
  }
  int res = 1;
  for (int i = 2; i <= 100000; i++) {
    if (!pr[i]) {
      int prev = pos[i];
      for (int j = 2 * i; j <= 100000; j += i) {
        pr[j] = true;
        if (pos[j] != -1) {
          if (prev != -1) {
            adj[prev].push_back(pos[j]);
          }
          prev = pos[j];
        }
      }
    }
  }
  for (int i = n - 1; i >= 0; i--) {
    mem[i] = 1;
    for (int j = 0; j < adj[i].size(); j++) {
      mem[i] = max(mem[i], mem[adj[i][j]] + 1);
    }
    res = max(res, mem[i]);
  }
  cout << res << endl;
  return 0;
}

### Prompt

Your challenge is to write 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 n;
int pos[100010];
int mem[100010];
bool pr[100010];
vector<int> adj[100010];
int main() {
  memset(pos, -1, sizeof pos);
  cin >> n;
  for (int i = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    pos[a] = i;
  }
  int res = 1;
  for (int i = 2; i <= 100000; i++) {
    if (!pr[i]) {
      int prev = pos[i];
      for (int j = 2 * i; j <= 100000; j += i) {
        pr[j] = true;
        if (pos[j] != -1) {
          if (prev != -1) {
            adj[prev].push_back(pos[j]);
          }
          prev = pos[j];
        }
      }
    }
  }
  for (int i = n - 1; i >= 0; i--) {
    mem[i] = 1;
    for (int j = 0; j < adj[i].size(); j++) {
      mem[i] = max(mem[i], mem[adj[i][j]] + 1);
    }
    res = max(res, mem[i]);
  }
  cout << res << endl;
  return 0;
}

```