#include <bits/stdc++.h>
using namespace std;
const long long lt = 100005;
long long mod = 1000000007;
vector<long long> factors[100005];
void seive() {
  long long i, j;
  for (i = 2; i <= 100000; i++)
    for (j = i; j <= 100000; j += i) factors[j].push_back(i);
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> a;
  long long i, val;
  for (i = 0; i < n; i++) {
    cin >> val;
    a.push_back(val);
  }
  seive();
  vector<long long> dp(100005, 0);
  for (i = 0; i < n; i++) {
    if (a[i] == 1) continue;
    long long j;
    long long mx = 1;
    for (j = 0; j < (long long)(factors[a[i]]).size(); j++) {
      long long x = factors[a[i]][j];
      mx = max(mx, 1 + dp[x]);
    }
    for (j = 0; j < (long long)(factors[a[i]]).size(); j++) {
      long long x = factors[a[i]][j];
      dp[x] = max(mx, dp[x]);
    }
  }
  long long ans = 1;
  for (i = 2; i <= 100000; i++) ans = max(ans, dp[i]);
  cout << ans << endl;
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 lt = 100005;
long long mod = 1000000007;
vector<long long> factors[100005];
void seive() {
  long long i, j;
  for (i = 2; i <= 100000; i++)
    for (j = i; j <= 100000; j += i) factors[j].push_back(i);
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> a;
  long long i, val;
  for (i = 0; i < n; i++) {
    cin >> val;
    a.push_back(val);
  }
  seive();
  vector<long long> dp(100005, 0);
  for (i = 0; i < n; i++) {
    if (a[i] == 1) continue;
    long long j;
    long long mx = 1;
    for (j = 0; j < (long long)(factors[a[i]]).size(); j++) {
      long long x = factors[a[i]][j];
      mx = max(mx, 1 + dp[x]);
    }
    for (j = 0; j < (long long)(factors[a[i]]).size(); j++) {
      long long x = factors[a[i]][j];
      dp[x] = max(mx, dp[x]);
    }
  }
  long long ans = 1;
  for (i = 2; i <= 100000; i++) ans = max(ans, dp[i]);
  cout << ans << endl;
  return 0;
}

```