#include <bits/stdc++.h>
using namespace std;
vector<long long int> pf[200000];
long long a[200000];
void seive() {
  pf[1].push_back(1);
  for (long long i = 0; i < 200000; i++) a[i] = 0;
  for (long long i = 2; i <= 100000; i++) {
    if (a[i] == 0) {
      for (long long j = i; j <= 100000; j += i) {
        a[j] = 1;
        pf[j].push_back(i);
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  seive();
  while (TESTS--) {
    long long i, j, k, l, m, n;
    long long b[200000], ans[200000], aa;
    aa = 0;
    for (i = 0; i < 200000; i++) ans[i] = -1;
    cin >> n;
    for (i = 0; i < n; i++) cin >> b[i];
    for (i = n - 1; i >= 0; i--) {
      k = 1;
      for (auto j : pf[b[i]]) {
        k = max(ans[j] + 1, k);
      }
      for (auto j : pf[b[i]]) {
        ans[j] = max(ans[j], k);
        aa = max(aa, ans[j]);
      }
    }
    cout << aa;
  }
  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;
vector<long long int> pf[200000];
long long a[200000];
void seive() {
  pf[1].push_back(1);
  for (long long i = 0; i < 200000; i++) a[i] = 0;
  for (long long i = 2; i <= 100000; i++) {
    if (a[i] == 0) {
      for (long long j = i; j <= 100000; j += i) {
        a[j] = 1;
        pf[j].push_back(i);
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  seive();
  while (TESTS--) {
    long long i, j, k, l, m, n;
    long long b[200000], ans[200000], aa;
    aa = 0;
    for (i = 0; i < 200000; i++) ans[i] = -1;
    cin >> n;
    for (i = 0; i < n; i++) cin >> b[i];
    for (i = n - 1; i >= 0; i--) {
      k = 1;
      for (auto j : pf[b[i]]) {
        k = max(ans[j] + 1, k);
      }
      for (auto j : pf[b[i]]) {
        ans[j] = max(ans[j], k);
        aa = max(aa, ans[j]);
      }
    }
    cout << aa;
  }
  return 0;
}

```