#include <bits/stdc++.h>
using namespace std;
long long n, arr[100000 + 5];
long long sp[100000 + 5];
long long dp[100000 + 5];
long long d[100000 + 5], ans;
void pre() {
  for (long long i = (long long)(2); i <= (long long)(100000); i++) {
    if (sp[i] != 0) continue;
    sp[i] = i;
    for (long long j = i + i; j <= 100000; j += i) sp[j] = i;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  pre();
  cin >> n;
  for (long long i = (long long)(1); i <= (long long)(n); i++) cin >> arr[i];
  if (n == 1) {
    cout << "1" << endl;
    return 0;
  }
  for (long long i = (long long)(1); i <= (long long)(n); i++) {
    long long tmp = arr[i];
    while (tmp != 1) {
      dp[arr[i]] = max(dp[arr[i]], d[sp[tmp]] + 1);
      tmp = tmp / sp[tmp];
    }
    tmp = arr[i];
    while (tmp != 1) {
      d[sp[tmp]] = dp[arr[i]];
      tmp = tmp / sp[tmp];
    }
  }
  for (long long i = (long long)(1); i <= (long long)(n); i++)
    ans = max(ans, dp[arr[i]]);
  cout << ans << endl;
  return 0;
}

### 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 n, arr[100000 + 5];
long long sp[100000 + 5];
long long dp[100000 + 5];
long long d[100000 + 5], ans;
void pre() {
  for (long long i = (long long)(2); i <= (long long)(100000); i++) {
    if (sp[i] != 0) continue;
    sp[i] = i;
    for (long long j = i + i; j <= 100000; j += i) sp[j] = i;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  pre();
  cin >> n;
  for (long long i = (long long)(1); i <= (long long)(n); i++) cin >> arr[i];
  if (n == 1) {
    cout << "1" << endl;
    return 0;
  }
  for (long long i = (long long)(1); i <= (long long)(n); i++) {
    long long tmp = arr[i];
    while (tmp != 1) {
      dp[arr[i]] = max(dp[arr[i]], d[sp[tmp]] + 1);
      tmp = tmp / sp[tmp];
    }
    tmp = arr[i];
    while (tmp != 1) {
      d[sp[tmp]] = dp[arr[i]];
      tmp = tmp / sp[tmp];
    }
  }
  for (long long i = (long long)(1); i <= (long long)(n); i++)
    ans = max(ans, dp[arr[i]]);
  cout << ans << endl;
  return 0;
}

```