#include <bits/stdc++.h>
using namespace std;
const long long int maxn = (1e6) + 1;
const long long int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  long long int a[n], i, j, k;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long int ans = 1;
  vector<long long int> dp(maxn, 0);
  for (i = 0; i < n; i++) {
    long long int x = a[i];
    vector<long long int> fact;
    for (j = 2; j * j <= x; j++) {
      if (x % j == 0) fact.push_back(j);
      while (x % j == 0) {
        x = x / j;
      }
    }
    if (x >= 2) fact.push_back(x);
    for (auto f : fact) {
      dp[f] += 1;
    }
    long long int mx = 0;
    for (auto f : fact) {
      mx = max(dp[f], mx);
    }
    for (auto f : fact) {
      dp[f] = max(mx, dp[f]);
    }
  }
  for (i = 0; i < dp.size(); i++) {
    ans = max(ans, dp[i]);
  }
  cout << ans << "\n";
  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;
const long long int maxn = (1e6) + 1;
const long long int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n;
  cin >> n;
  long long int a[n], i, j, k;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long int ans = 1;
  vector<long long int> dp(maxn, 0);
  for (i = 0; i < n; i++) {
    long long int x = a[i];
    vector<long long int> fact;
    for (j = 2; j * j <= x; j++) {
      if (x % j == 0) fact.push_back(j);
      while (x % j == 0) {
        x = x / j;
      }
    }
    if (x >= 2) fact.push_back(x);
    for (auto f : fact) {
      dp[f] += 1;
    }
    long long int mx = 0;
    for (auto f : fact) {
      mx = max(dp[f], mx);
    }
    for (auto f : fact) {
      dp[f] = max(mx, dp[f]);
    }
  }
  for (i = 0; i < dp.size(); i++) {
    ans = max(ans, dp[i]);
  }
  cout << ans << "\n";
  return 0;
}

```