#include <bits/stdc++.h>
using namespace std;
const long long int Mod = 1e9 + 7;
const long long int M1 = 998244353;
long long int mod(long long int n) { return ((n % Mod) + Mod) % Mod; }
long long int power(long long int x, long long int y) {
  long long int res = 1;
  x = x;
  while (y > 0) {
    if (y & 1) res = mod(res * x);
    x = mod(x * x);
    y = mod(y >> 1);
  }
  return mod(res);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<long long int> v(n);
  for (long long int i = 0; i < n; i++) cin >> v[i];
  vector<long long int> dp(100005, 0);
  long long int ans = 0;
  for (long long int i = 0; i < n; i++) {
    long long int x = v[i];
    vector<long long int> d;
    for (long long int i = 2; i * i <= x; i++) {
      if (x % i == 0) {
        d.push_back(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) d.push_back(x);
    long long int mx = 0;
    for (long long int i = 0; i < d.size(); i++) {
      mx = max(mx, dp[d[i]]);
    }
    mx++;
    for (auto p : d) {
      dp[p] = mx;
    }
    ans = max(mx, ans);
  }
  cout << ans << '\n';
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 Mod = 1e9 + 7;
const long long int M1 = 998244353;
long long int mod(long long int n) { return ((n % Mod) + Mod) % Mod; }
long long int power(long long int x, long long int y) {
  long long int res = 1;
  x = x;
  while (y > 0) {
    if (y & 1) res = mod(res * x);
    x = mod(x * x);
    y = mod(y >> 1);
  }
  return mod(res);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<long long int> v(n);
  for (long long int i = 0; i < n; i++) cin >> v[i];
  vector<long long int> dp(100005, 0);
  long long int ans = 0;
  for (long long int i = 0; i < n; i++) {
    long long int x = v[i];
    vector<long long int> d;
    for (long long int i = 2; i * i <= x; i++) {
      if (x % i == 0) {
        d.push_back(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) d.push_back(x);
    long long int mx = 0;
    for (long long int i = 0; i < d.size(); i++) {
      mx = max(mx, dp[d[i]]);
    }
    mx++;
    for (auto p : d) {
      dp[p] = mx;
    }
    ans = max(mx, ans);
  }
  cout << ans << '\n';
}

```