#include <bits/stdc++.h>
using namespace std;
int good[100005], dp[100005], d[100005];
set<int> g;
void print(int n) {
  for (int i = 0; i <= n; i++) {
    cout << dp[i] << " ";
  }
  cout << "\n";
  for (int i = 0; i <= 2 * n; i++) {
    cout << d[i] << " ";
  }
  cout << "\n\n";
}
int main() {
  int n;
  cin >> n;
  memset(dp, 0, sizeof(dp));
  memset(d, 0, sizeof(d));
  for (int i = 0; i < n; i++) {
    cin >> good[i];
  }
  int s;
  int rta = 0;
  for (int i = 0; i < n; i++) {
    vector<int> divs;
    s = sqrt(good[i]);
    for (int j = 1; j <= s; j++) {
      if (good[i] % j == 0) {
        if (j > 1) {
          divs.push_back(j);
          dp[i] = max(d[j] + 1, dp[i]);
        }
        if (j * j != good[i]) {
          divs.push_back(good[i] / j);
          dp[i] = max(d[good[i] / j] + 1, dp[i]);
        }
      }
    }
    dp[i] = max(dp[i], 1);
    for (auto x : divs) {
      d[x] = max(d[x], dp[i]);
    }
    rta = max(rta, dp[i]);
  }
  cout << rta << "\n";
}

### Prompt

Please provide a cpp coded solution 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 good[100005], dp[100005], d[100005];
set<int> g;
void print(int n) {
  for (int i = 0; i <= n; i++) {
    cout << dp[i] << " ";
  }
  cout << "\n";
  for (int i = 0; i <= 2 * n; i++) {
    cout << d[i] << " ";
  }
  cout << "\n\n";
}
int main() {
  int n;
  cin >> n;
  memset(dp, 0, sizeof(dp));
  memset(d, 0, sizeof(d));
  for (int i = 0; i < n; i++) {
    cin >> good[i];
  }
  int s;
  int rta = 0;
  for (int i = 0; i < n; i++) {
    vector<int> divs;
    s = sqrt(good[i]);
    for (int j = 1; j <= s; j++) {
      if (good[i] % j == 0) {
        if (j > 1) {
          divs.push_back(j);
          dp[i] = max(d[j] + 1, dp[i]);
        }
        if (j * j != good[i]) {
          divs.push_back(good[i] / j);
          dp[i] = max(d[good[i] / j] + 1, dp[i]);
        }
      }
    }
    dp[i] = max(dp[i], 1);
    for (auto x : divs) {
      d[x] = max(d[x], dp[i]);
    }
    rta = max(rta, dp[i]);
  }
  cout << rta << "\n";
}

```