#include <bits/stdc++.h>
using namespace std;
long long n;
long long arr[100005], dp[100005];
void solve() {
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  if (n == 1) {
    cout << 1;
    return;
  }
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    vector<long long> v;
    for (long long j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) v.push_back(j);
      while (arr[i] % j == 0) arr[i] /= j;
    }
    if (arr[i] != 1) v.push_back(arr[i]);
    long long temp = 0;
    for (long long j = 0; j < v.size(); j++) {
      dp[v[j]]++;
      temp = max(temp, dp[v[j]]);
    }
    for (long long j = 0; j < v.size(); j++) dp[v[j]] = temp;
    ans = max(ans, temp);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) solve();
  return 0;
}

### Prompt

Please create a solution in CPP 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;
long long n;
long long arr[100005], dp[100005];
void solve() {
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
  }
  if (n == 1) {
    cout << 1;
    return;
  }
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    vector<long long> v;
    for (long long j = 2; j <= sqrt(arr[i]); j++) {
      if (arr[i] % j == 0) v.push_back(j);
      while (arr[i] % j == 0) arr[i] /= j;
    }
    if (arr[i] != 1) v.push_back(arr[i]);
    long long temp = 0;
    for (long long j = 0; j < v.size(); j++) {
      dp[v[j]]++;
      temp = max(temp, dp[v[j]]);
    }
    for (long long j = 0; j < v.size(); j++) dp[v[j]] = temp;
    ans = max(ans, temp);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) solve();
  return 0;
}

```