#include <bits/stdc++.h>
using namespace std;
int a[1000 * 100 + 100], n;
int calc(int x) {
  int y = x, Max = 0;
  for (int i = 2; i <= sqrt(x); i++)
    if (x % i == 0) {
      while (x % i == 0) {
        x /= i;
      }
      if (a[i] != 0) Max = max(Max, a[i]);
    }
  if (x != 1 && x != y) Max = max(Max, a[x]);
  Max++;
  x = y;
  for (int i = 2; i <= sqrt(x); i++)
    if (x % i == 0) {
      while (x % i == 0) {
        x /= i;
      }
      a[i] = max(a[i], Max);
    }
  if (x != 1 && x != y) a[x] = max(a[x], Max);
  Max--;
  return Max;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  vector<int> v;
  for (int i = 1; i <= n; i++) {
    int t;
    cin >> t;
    a[t] = 1;
    v.push_back(t);
  }
  for (int i = 2; i <= 1000 * 100; i++)
    if (a[i] != 0) {
      a[i] += calc(i);
    }
  int Max = -1;
  for (int i = 0; i < v.size(); i++) Max = max(Max, a[v[i]]);
  cout << Max;
}

### 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 a[1000 * 100 + 100], n;
int calc(int x) {
  int y = x, Max = 0;
  for (int i = 2; i <= sqrt(x); i++)
    if (x % i == 0) {
      while (x % i == 0) {
        x /= i;
      }
      if (a[i] != 0) Max = max(Max, a[i]);
    }
  if (x != 1 && x != y) Max = max(Max, a[x]);
  Max++;
  x = y;
  for (int i = 2; i <= sqrt(x); i++)
    if (x % i == 0) {
      while (x % i == 0) {
        x /= i;
      }
      a[i] = max(a[i], Max);
    }
  if (x != 1 && x != y) a[x] = max(a[x], Max);
  Max--;
  return Max;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  vector<int> v;
  for (int i = 1; i <= n; i++) {
    int t;
    cin >> t;
    a[t] = 1;
    v.push_back(t);
  }
  for (int i = 2; i <= 1000 * 100; i++)
    if (a[i] != 0) {
      a[i] += calc(i);
    }
  int Max = -1;
  for (int i = 0; i < v.size(); i++) Max = max(Max, a[v[i]]);
  cout << Max;
}

```