#include <bits/stdc++.h>
using namespace std;
void div(vector<int> &divisors, int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      divisors.push_back(i);
      if (x / i != i) divisors.push_back(x / i);
    }
  }
  divisors.push_back(x);
}
int main() {
  int n;
  cin >> n;
  int dp[100005] = {}, d[100005] = {};
  for (int i = 0; i < n; i++) {
    vector<int> divisors;
    int x;
    cin >> x;
    if (x == 1) continue;
    div(divisors, x);
    for (int j = 0; j < divisors.size(); j++)
      dp[x] = max(dp[x], d[divisors[j]] + 1);
    for (int j = 0; j < divisors.size(); j++) d[divisors[j]] = dp[x];
  }
  int ans = 1;
  for (int i = 1; i <= 100004; i++) ans = max(ans, dp[i]);
  cout << ans << endl;
}

### 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;
void div(vector<int> &divisors, int x) {
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      divisors.push_back(i);
      if (x / i != i) divisors.push_back(x / i);
    }
  }
  divisors.push_back(x);
}
int main() {
  int n;
  cin >> n;
  int dp[100005] = {}, d[100005] = {};
  for (int i = 0; i < n; i++) {
    vector<int> divisors;
    int x;
    cin >> x;
    if (x == 1) continue;
    div(divisors, x);
    for (int j = 0; j < divisors.size(); j++)
      dp[x] = max(dp[x], d[divisors[j]] + 1);
    for (int j = 0; j < divisors.size(); j++) d[divisors[j]] = dp[x];
  }
  int ans = 1;
  for (int i = 1; i <= 100004; i++) ans = max(ans, dp[i]);
  cout << ans << endl;
}

```