#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e5 + 1;
vector<int> decompose(int num) {
  vector<int> components;
  for (int i = 2; i * i <= num; i++) {
    if (num % i == 0) {
      components.push_back(i);
      while (num % i == 0) {
        num /= i;
      }
    }
  }
  if (num > 1) components.push_back(num);
  return components;
}
int main() {
  int N;
  cin >> N;
  vector<int> nums(N);
  for (auto& num : nums) cin >> num;
  vector<int> max_lens(MAX);
  vector<int> results(N);
  for (int i = N - 1; i >= 0; i--) {
    auto components = decompose(nums[i]);
    int maximum = INT_MIN;
    for (auto& component : components) {
      maximum = max(maximum, max_lens[component]);
    }
    results[i] = 1;
    if (maximum != INT_MIN) results[i] += maximum;
    for (auto& component : components) {
      max_lens[component] = results[i];
    }
  }
  int maximum = INT_MIN;
  for (auto result : results) maximum = max(result, maximum);
  cout << maximum << 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;
const int MAX = 1e5 + 1;
vector<int> decompose(int num) {
  vector<int> components;
  for (int i = 2; i * i <= num; i++) {
    if (num % i == 0) {
      components.push_back(i);
      while (num % i == 0) {
        num /= i;
      }
    }
  }
  if (num > 1) components.push_back(num);
  return components;
}
int main() {
  int N;
  cin >> N;
  vector<int> nums(N);
  for (auto& num : nums) cin >> num;
  vector<int> max_lens(MAX);
  vector<int> results(N);
  for (int i = N - 1; i >= 0; i--) {
    auto components = decompose(nums[i]);
    int maximum = INT_MIN;
    for (auto& component : components) {
      maximum = max(maximum, max_lens[component]);
    }
    results[i] = 1;
    if (maximum != INT_MIN) results[i] += maximum;
    for (auto& component : components) {
      max_lens[component] = results[i];
    }
  }
  int maximum = INT_MIN;
  for (auto result : results) maximum = max(result, maximum);
  cout << maximum << endl;
  return 0;
}

```