#include <bits/stdc++.h>
using namespace std;
int gcd(int a, int b) { return (!b) ? a : gcd(b, a % b); }
set<int> bolenler(int a) {
  set<int> qaa;
ella:
  int kok = sqrt(a);
  for (int i = 2; i <= kok; i++) {
    if (!(a % i)) {
      qaa.insert(i);
      a /= i;
      goto ella;
    }
  }
  qaa.insert(a);
  return qaa;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  int best_case[100011] = {};
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int eded;
    cin >> eded;
    set<int> cavab = bolenler(eded);
    set<int>::iterator it = cavab.begin();
    int maxx = 1;
    while (it != cavab.end()) {
      if (best_case[(*it)] + 1 > maxx) maxx = best_case[(*it)] + 1;
      ++it;
    }
    it = cavab.begin();
    while (it != cavab.end()) {
      best_case[*it] = maxx;
      ++it;
    }
  }
  int maxx = 0;
  for (int i = 0; i < 100011; i++) maxx = max(maxx, best_case[i]);
  cout << maxx;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 gcd(int a, int b) { return (!b) ? a : gcd(b, a % b); }
set<int> bolenler(int a) {
  set<int> qaa;
ella:
  int kok = sqrt(a);
  for (int i = 2; i <= kok; i++) {
    if (!(a % i)) {
      qaa.insert(i);
      a /= i;
      goto ella;
    }
  }
  qaa.insert(a);
  return qaa;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  int best_case[100011] = {};
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int eded;
    cin >> eded;
    set<int> cavab = bolenler(eded);
    set<int>::iterator it = cavab.begin();
    int maxx = 1;
    while (it != cavab.end()) {
      if (best_case[(*it)] + 1 > maxx) maxx = best_case[(*it)] + 1;
      ++it;
    }
    it = cavab.begin();
    while (it != cavab.end()) {
      best_case[*it] = maxx;
      ++it;
    }
  }
  int maxx = 0;
  for (int i = 0; i < 100011; i++) maxx = max(maxx, best_case[i]);
  cout << maxx;
}

```