#include <bits/stdc++.h>
using namespace std;
bool solve() {
  int n = 100000, a, ans = 0;
  if (scanf("%d", &n) == EOF) return false;
  vector<int> mem(n), bs(100001, -1);
  for (int i = 0; i < n; ++i) {
    a = i + 1;
    scanf("%d", &a);
    int best_n = 0;
    vector<int> b;
    for (int j = 2; j * j <= a; ++j) {
      if (a % j == 0) {
        while (a % j == 0) a /= j;
        best_n = max(bs[j], best_n);
        b.push_back(j);
      }
    }
    if (a > 1) {
      best_n = max(bs[a], best_n);
      b.push_back(a);
    }
    for (size_t j = 0; j < b.size(); ++j) {
      bs[b[j]] = best_n + 1;
    }
    ans = max(ans, best_n + 1);
  }
  printf("%d\n", ans);
  return true;
}
int main() {
  solve();
  return 0;
}

### 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;
bool solve() {
  int n = 100000, a, ans = 0;
  if (scanf("%d", &n) == EOF) return false;
  vector<int> mem(n), bs(100001, -1);
  for (int i = 0; i < n; ++i) {
    a = i + 1;
    scanf("%d", &a);
    int best_n = 0;
    vector<int> b;
    for (int j = 2; j * j <= a; ++j) {
      if (a % j == 0) {
        while (a % j == 0) a /= j;
        best_n = max(bs[j], best_n);
        b.push_back(j);
      }
    }
    if (a > 1) {
      best_n = max(bs[a], best_n);
      b.push_back(a);
    }
    for (size_t j = 0; j < b.size(); ++j) {
      bs[b[j]] = best_n + 1;
    }
    ans = max(ans, best_n + 1);
  }
  printf("%d\n", ans);
  return true;
}
int main() {
  solve();
  return 0;
}

```