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

### Prompt

Your task is to create 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() {
  int n, arr[100001], divisor[100001], dp[100001], ans = 0;
  memset(dp, 0, sizeof(dp));
  memset(divisor, 0, sizeof(divisor));
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    dp[i] = 1;
    int nrep = sqrt(arr[i]);
    for (int j = 2; j <= nrep; ++j) {
      if (arr[i] % j != 0) continue;
      dp[i] = max(dp[i], divisor[j] + 1);
      dp[i] = max(dp[i], divisor[arr[i] / j] + 1);
    }
    for (int j = 2; j <= nrep; ++j) {
      if (arr[i] % j != 0) continue;
      divisor[j] = dp[i];
      divisor[arr[i] / j] = dp[i];
    }
    divisor[arr[i]] = dp[i];
    ans = max(ans, dp[i]);
  }
  cout << ans;
}

```