#include <bits/stdc++.h>
using namespace std;
int main() {
  long long int n;
  cin >> n;
  long long int ans[100001];
  for (long long int i = 0; i < 100001; i++) ans[i] = -1;
  long long int arr[n];
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
    ans[arr[i]] = 1;
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) {
        ans[arr[i]] = max(ans[arr[i]], max(ans[j], ans[arr[i] / j]) + 1);
      }
    }
    for (long long int j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) {
        ans[j] = ans[arr[i]];
        ans[arr[i] / j] = ans[arr[i]];
      }
    }
  }
  long long int k = 1;
  for (long long int i = 0; i < n; i++) k = max(k, ans[arr[i]]);
  cout << k;
}

### Prompt

Generate 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() {
  long long int n;
  cin >> n;
  long long int ans[100001];
  for (long long int i = 0; i < 100001; i++) ans[i] = -1;
  long long int arr[n];
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
    ans[arr[i]] = 1;
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) {
        ans[arr[i]] = max(ans[arr[i]], max(ans[j], ans[arr[i] / j]) + 1);
      }
    }
    for (long long int j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) {
        ans[j] = ans[arr[i]];
        ans[arr[i] / j] = ans[arr[i]];
      }
    }
  }
  long long int k = 1;
  for (long long int i = 0; i < n; i++) k = max(k, ans[arr[i]]);
  cout << k;
}

```