#include <bits/stdc++.h>
using namespace std;
long long spf[100005];
void sieve() {
  spf[1] = 1;
  for (long long i = 2; i < 100005; i++) {
    spf[i] = i;
  }
  for (long long i = 4; i < 100005; i += 2) {
    spf[i] = 2;
  }
  for (long long i = 3; i * i < 100005; i++) {
    if (spf[i] == i) {
      for (long long j = i * i; j < 100005; j += i) {
        if (spf[j] == j) spf[j] = i;
      }
    }
  }
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  sieve();
  vector<long long> dp(n);
  vector<long long> make_pair(100005, 0);
  long long ans = 1;
  for (long long i = 0; i < n; i++) {
    long long t = a[i];
    set<long long> pf;
    while (t != 1) {
      pf.insert(spf[t]);
      t = t / spf[t];
    }
    long long mx = 0;
    for (auto x : pf) {
      mx = max(mx, make_pair[x]);
    }
    for (auto x : pf) {
      make_pair[x] = max(make_pair[x], mx + 1);
    }
    ans = max(mx + 1, ans);
  }
  cout << ans << "\n";
}

### Prompt

Create a solution in cpp for 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 spf[100005];
void sieve() {
  spf[1] = 1;
  for (long long i = 2; i < 100005; i++) {
    spf[i] = i;
  }
  for (long long i = 4; i < 100005; i += 2) {
    spf[i] = 2;
  }
  for (long long i = 3; i * i < 100005; i++) {
    if (spf[i] == i) {
      for (long long j = i * i; j < 100005; j += i) {
        if (spf[j] == j) spf[j] = i;
      }
    }
  }
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  sieve();
  vector<long long> dp(n);
  vector<long long> make_pair(100005, 0);
  long long ans = 1;
  for (long long i = 0; i < n; i++) {
    long long t = a[i];
    set<long long> pf;
    while (t != 1) {
      pf.insert(spf[t]);
      t = t / spf[t];
    }
    long long mx = 0;
    for (auto x : pf) {
      mx = max(mx, make_pair[x]);
    }
    for (auto x : pf) {
      make_pair[x] = max(make_pair[x], mx + 1);
    }
    ans = max(mx + 1, ans);
  }
  cout << ans << "\n";
}

```