#include <bits/stdc++.h>
const int cmaxn = 100010;
std::vector<int> a, sep(cmaxn), dp(cmaxn);
void init() {
  for (int i = 2; i < cmaxn; i++) {
    if (!sep[i]) {
      for (int j = i; j < cmaxn; j += i) {
        sep[j] = i;
      }
    }
  }
}
int main() {
  int n;
  std::cin >> n;
  init();
  for (int i = 0; i < n; i++) {
    int tmp;
    std::cin >> tmp;
    a.push_back(tmp);
  }
  sort(a.begin(), a.end());
  int answer = 0;
  for (int i = 0; i < n; i++) {
    int mx_cnt = 0;
    for (int j = a[i]; j > 1; j /= sep[j])
      mx_cnt = std::max(mx_cnt, dp[sep[j]] + 1);
    for (int j = a[i]; j > 1; j /= sep[j])
      dp[sep[j]] = std::max(dp[sep[j]], mx_cnt);
    answer = std::max(answer, mx_cnt);
  }
  if (n == 1) {
    answer = 1;
  }
  std::cout << answer;
  return 0;
}

### Prompt

Your task is to create a CPP solution to 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>
const int cmaxn = 100010;
std::vector<int> a, sep(cmaxn), dp(cmaxn);
void init() {
  for (int i = 2; i < cmaxn; i++) {
    if (!sep[i]) {
      for (int j = i; j < cmaxn; j += i) {
        sep[j] = i;
      }
    }
  }
}
int main() {
  int n;
  std::cin >> n;
  init();
  for (int i = 0; i < n; i++) {
    int tmp;
    std::cin >> tmp;
    a.push_back(tmp);
  }
  sort(a.begin(), a.end());
  int answer = 0;
  for (int i = 0; i < n; i++) {
    int mx_cnt = 0;
    for (int j = a[i]; j > 1; j /= sep[j])
      mx_cnt = std::max(mx_cnt, dp[sep[j]] + 1);
    for (int j = a[i]; j > 1; j /= sep[j])
      dp[sep[j]] = std::max(dp[sep[j]], mx_cnt);
    answer = std::max(answer, mx_cnt);
  }
  if (n == 1) {
    answer = 1;
  }
  std::cout << answer;
  return 0;
}

```