#include <bits/stdc++.h>
using namespace std;
int n;
int cant[100300];
int inf = 1 << 30;
int ct;
set<int> v;
int primes[100003];
int primo[100003];
set<int> todos[100300];
void criba() {
  memset(primes, -1, sizeof primes);
  primes[1] = 1;
  for (int i = 2; i <= 100000; i++) {
    if (primes[i] == -1) {
      for (int j = i; j <= 100000; j += i) {
        if (primes[j] == -1) primes[j] = i;
        todos[j].insert(i);
      }
      primes[i] = 1;
    }
  }
}
int arr[100300];
int main() {
  criba();
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  int res = 1;
  set<int> primos;
  int p;
  for (int i = n - 1; i >= 0; i--) {
    int rr = 1;
    for (typeof todos[arr[i]].begin() it = todos[arr[i]].begin();
         it != todos[arr[i]].end(); it++) {
      p = *it;
      if (p == 1) continue;
      cant[p]++;
      if (cant[p] > rr) rr = cant[p];
    }
    for (typeof todos[arr[i]].begin() it = todos[arr[i]].begin();
         it != todos[arr[i]].end(); it++) {
      p = *it;
      if (p == 1) continue;
      cant[p] = rr;
    }
    res = max(res, rr);
  }
  cout << res << endl;
  return 0;
}

### Prompt

Develop a solution in Cpp 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 n;
int cant[100300];
int inf = 1 << 30;
int ct;
set<int> v;
int primes[100003];
int primo[100003];
set<int> todos[100300];
void criba() {
  memset(primes, -1, sizeof primes);
  primes[1] = 1;
  for (int i = 2; i <= 100000; i++) {
    if (primes[i] == -1) {
      for (int j = i; j <= 100000; j += i) {
        if (primes[j] == -1) primes[j] = i;
        todos[j].insert(i);
      }
      primes[i] = 1;
    }
  }
}
int arr[100300];
int main() {
  criba();
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  int res = 1;
  set<int> primos;
  int p;
  for (int i = n - 1; i >= 0; i--) {
    int rr = 1;
    for (typeof todos[arr[i]].begin() it = todos[arr[i]].begin();
         it != todos[arr[i]].end(); it++) {
      p = *it;
      if (p == 1) continue;
      cant[p]++;
      if (cant[p] > rr) rr = cant[p];
    }
    for (typeof todos[arr[i]].begin() it = todos[arr[i]].begin();
         it != todos[arr[i]].end(); it++) {
      p = *it;
      if (p == 1) continue;
      cant[p] = rr;
    }
    res = max(res, rr);
  }
  cout << res << endl;
  return 0;
}

```