#include <bits/stdc++.h>
using namespace std;
int main() {
  vector<int> primes;
  vector<bool> check(100001, true);
  for (int i = 2; i * i <= 100000; i++) {
    if (check[i] == true) {
      for (int j = i + i; j <= 100000; j += i) {
        check[j] = false;
      }
    }
  }
  for (int i = 2; i <= 100000; i++) {
    if (check[i] == true) {
      primes.push_back(i);
    }
  }
  int n, maxi = 1;
  scanf("%d", &n);
  vector<int> a(n), remember(primes[primes.size() - 1] + 1, 0);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    int tmpmax = 0;
    vector<int> p;
    if (check[a[i]] == false) {
      for (unsigned int j = 0; primes[j] * 2 <= a[i] && j < primes.size();
           j++) {
        if (a[i] % primes[j] == 0) {
          tmpmax = max(tmpmax, remember[primes[j]]);
          p.push_back(primes[j]);
        }
      }
    } else {
      remember[a[i]] = 1;
    }
    tmpmax++;
    for (unsigned int k = 0; k < p.size(); k++) {
      remember[p[k]] = tmpmax;
    }
    maxi = max(maxi, tmpmax);
  }
  printf("%d\n", maxi);
  return 0;
}

### Prompt

Generate 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>
using namespace std;
int main() {
  vector<int> primes;
  vector<bool> check(100001, true);
  for (int i = 2; i * i <= 100000; i++) {
    if (check[i] == true) {
      for (int j = i + i; j <= 100000; j += i) {
        check[j] = false;
      }
    }
  }
  for (int i = 2; i <= 100000; i++) {
    if (check[i] == true) {
      primes.push_back(i);
    }
  }
  int n, maxi = 1;
  scanf("%d", &n);
  vector<int> a(n), remember(primes[primes.size() - 1] + 1, 0);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    int tmpmax = 0;
    vector<int> p;
    if (check[a[i]] == false) {
      for (unsigned int j = 0; primes[j] * 2 <= a[i] && j < primes.size();
           j++) {
        if (a[i] % primes[j] == 0) {
          tmpmax = max(tmpmax, remember[primes[j]]);
          p.push_back(primes[j]);
        }
      }
    } else {
      remember[a[i]] = 1;
    }
    tmpmax++;
    for (unsigned int k = 0; k < p.size(); k++) {
      remember[p[k]] = tmpmax;
    }
    maxi = max(maxi, tmpmax);
  }
  printf("%d\n", maxi);
  return 0;
}

```