#include <bits/stdc++.h>
using namespace std;
int N, good;
bool prime[100010];
vector<int> fact, num, lis;
int main() {
  memset(prime, true, sizeof(prime));
  for (int i = 2; i * i <= 100000; i++)
    if (prime[i])
      for (int j = 2; i * j <= 100000; j++) prime[i * j] = false;
  for (int i = 2; i <= 100000; i++)
    if (prime[i]) {
      num.push_back(i);
      lis.push_back(0);
    }
  scanf("%d", &N);
  while (N--) {
    scanf("%d", &good);
    int temp = good;
    fact.clear();
    int longest = 0;
    for (int i = 0; i < num.size() && num[i] * num[i] <= good; i++)
      if (good % num[i] == 0) {
        fact.push_back(i);
        longest = max(longest, lis[i] + 1);
        while (temp % num[i] == 0) temp /= num[i];
      }
    if (temp > 1) {
      int i = lower_bound(num.begin(), num.end(), temp) - num.begin();
      fact.push_back(i);
      longest = max(longest, lis[i] + 1);
    }
    for (int i = 0; i < fact.size(); i++)
      lis[fact[i]] = max(lis[fact[i]], longest);
  }
  int ans = 1;
  for (int i = 0; i < num.size(); i++) ans = max(ans, lis[i]);
  printf("%d\n", ans);
  return 0;
}

### Prompt

In CPP, your task is to solve 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 N, good;
bool prime[100010];
vector<int> fact, num, lis;
int main() {
  memset(prime, true, sizeof(prime));
  for (int i = 2; i * i <= 100000; i++)
    if (prime[i])
      for (int j = 2; i * j <= 100000; j++) prime[i * j] = false;
  for (int i = 2; i <= 100000; i++)
    if (prime[i]) {
      num.push_back(i);
      lis.push_back(0);
    }
  scanf("%d", &N);
  while (N--) {
    scanf("%d", &good);
    int temp = good;
    fact.clear();
    int longest = 0;
    for (int i = 0; i < num.size() && num[i] * num[i] <= good; i++)
      if (good % num[i] == 0) {
        fact.push_back(i);
        longest = max(longest, lis[i] + 1);
        while (temp % num[i] == 0) temp /= num[i];
      }
    if (temp > 1) {
      int i = lower_bound(num.begin(), num.end(), temp) - num.begin();
      fact.push_back(i);
      longest = max(longest, lis[i] + 1);
    }
    for (int i = 0; i < fact.size(); i++)
      lis[fact[i]] = max(lis[fact[i]], longest);
  }
  int ans = 1;
  for (int i = 0; i < num.size(); i++) ans = max(ans, lis[i]);
  printf("%d\n", ans);
  return 0;
}

```