#include <bits/stdc++.h>
using namespace std;
int dp[100100] = {};
int p[100100] = {};
int main() {
  int n;
  int a[100100];
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  int lp = 1;
  p[1] = 2;
  for (int i = 3; i <= 100000; i += 2) {
    int tmp = 1;
    for (int j = 1; j <= lp; j++) {
      if (i % p[j] == 0) {
        tmp = 0;
        break;
      }
    }
    if (tmp == 1) {
      lp++;
      p[lp] = i;
    }
  }
  for (int i = 1; i <= n; i++) {
    int ans = 0;
    int tmp = a[i];
    for (int j = 1; j <= lp; j++) {
      while (tmp % p[j] == 0) {
        ans = max(ans, dp[j] + 1);
        tmp = tmp / p[j];
      }
      if (tmp < p[j]) break;
    }
    tmp = a[i];
    for (int j = 1; j <= lp; j++) {
      while (tmp % p[j] == 0) {
        dp[j] = ans;
        tmp = tmp / p[j];
      }
      if (tmp < p[j]) break;
    }
  }
  int mm = 0;
  for (int i = 1; i <= lp; i++) mm = max(mm, dp[i]);
  if (n == 1) mm = 1;
  cout << mm;
  return 0;
}

### Prompt

Please create a solution in Cpp 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>
using namespace std;
int dp[100100] = {};
int p[100100] = {};
int main() {
  int n;
  int a[100100];
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  int lp = 1;
  p[1] = 2;
  for (int i = 3; i <= 100000; i += 2) {
    int tmp = 1;
    for (int j = 1; j <= lp; j++) {
      if (i % p[j] == 0) {
        tmp = 0;
        break;
      }
    }
    if (tmp == 1) {
      lp++;
      p[lp] = i;
    }
  }
  for (int i = 1; i <= n; i++) {
    int ans = 0;
    int tmp = a[i];
    for (int j = 1; j <= lp; j++) {
      while (tmp % p[j] == 0) {
        ans = max(ans, dp[j] + 1);
        tmp = tmp / p[j];
      }
      if (tmp < p[j]) break;
    }
    tmp = a[i];
    for (int j = 1; j <= lp; j++) {
      while (tmp % p[j] == 0) {
        dp[j] = ans;
        tmp = tmp / p[j];
      }
      if (tmp < p[j]) break;
    }
  }
  int mm = 0;
  for (int i = 1; i <= lp; i++) mm = max(mm, dp[i]);
  if (n == 1) mm = 1;
  cout << mm;
  return 0;
}

```