#include <bits/stdc++.h>
using namespace std;
long long add(long long a, long long b) {
  a %= 1000000007;
  b %= 1000000007;
  long long res = ((a % 1000000007) + (b % 1000000007)) % 1000000007;
  return res % 1000000007;
}
long long mul(long long a, long long b) {
  long long res = (a) * (b);
  res %= 1000000007;
  if (res < 0) res += 1000000007;
  return res;
}
const long long N = 1e5 + 2;
long long f[N];
void solve() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) cin >> v[i];
  for (auto r : v) {
    long long temp = 1;
    for (long long i = 1; i * i <= r; i++) {
      if (r % i == 0) {
        if (i != 1) temp = max(temp, f[i] + 1);
        if (r / i != 1) temp = max(temp, f[r / i] + 1);
      }
    }
    for (long long i = 1; i * i <= r; i++) {
      if (r % i == 0) {
        f[i] = max(f[i], temp);
        f[r / i] = max(temp, f[r / i]);
      }
    }
  }
  long long ans = 0;
  for (long long i = 0; i < 1e5 + 1; i++) {
    ans = max(ans, f[i]);
  }
  cout << ans << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t = 1;
  while (t--) {
    solve();
  }
}

### 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 add(long long a, long long b) {
  a %= 1000000007;
  b %= 1000000007;
  long long res = ((a % 1000000007) + (b % 1000000007)) % 1000000007;
  return res % 1000000007;
}
long long mul(long long a, long long b) {
  long long res = (a) * (b);
  res %= 1000000007;
  if (res < 0) res += 1000000007;
  return res;
}
const long long N = 1e5 + 2;
long long f[N];
void solve() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) cin >> v[i];
  for (auto r : v) {
    long long temp = 1;
    for (long long i = 1; i * i <= r; i++) {
      if (r % i == 0) {
        if (i != 1) temp = max(temp, f[i] + 1);
        if (r / i != 1) temp = max(temp, f[r / i] + 1);
      }
    }
    for (long long i = 1; i * i <= r; i++) {
      if (r % i == 0) {
        f[i] = max(f[i], temp);
        f[r / i] = max(temp, f[r / i]);
      }
    }
  }
  long long ans = 0;
  for (long long i = 0; i < 1e5 + 1; i++) {
    ans = max(ans, f[i]);
  }
  cout << ans << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t = 1;
  while (t--) {
    solve();
  }
}

```