#include <bits/stdc++.h>
const int MAX = 100001;
int n;
using namespace std;
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  vector<int> Prime(MAX, -7);
  for (int i = 2; i < MAX; i++) {
    if (Prime[i] == -7) {
      Prime[i] = i;
      for (long long j = (long long)i * (long long)i; j < MAX; j += i) {
        Prime[j] = i;
      }
    }
  }
  cin >> n;
  vector<vector<int>> Del(n, vector<int>(0));
  for (int i = 0; i < n; i++) {
    int num;
    cin >> num;
    while (num > 1) {
      int cur = Prime[num];
      while (num % cur == 0) {
        num /= cur;
      }
      Del[i].push_back(cur);
    }
  }
  map<int, int> Dp;
  int res = 0;
  for (int i = 0; i < n; i++) {
    int ma = 1;
    for (auto j : Del[i]) {
      ma = max(ma, Dp[j] + 1);
    }
    for (auto j : Del[i]) {
      Dp[j] = ma;
    }
    res = max(res, ma);
  }
  cout << res;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 MAX = 100001;
int n;
using namespace std;
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  vector<int> Prime(MAX, -7);
  for (int i = 2; i < MAX; i++) {
    if (Prime[i] == -7) {
      Prime[i] = i;
      for (long long j = (long long)i * (long long)i; j < MAX; j += i) {
        Prime[j] = i;
      }
    }
  }
  cin >> n;
  vector<vector<int>> Del(n, vector<int>(0));
  for (int i = 0; i < n; i++) {
    int num;
    cin >> num;
    while (num > 1) {
      int cur = Prime[num];
      while (num % cur == 0) {
        num /= cur;
      }
      Del[i].push_back(cur);
    }
  }
  map<int, int> Dp;
  int res = 0;
  for (int i = 0; i < n; i++) {
    int ma = 1;
    for (auto j : Del[i]) {
      ma = max(ma, Dp[j] + 1);
    }
    for (auto j : Del[i]) {
      Dp[j] = ma;
    }
    res = max(res, ma);
  }
  cout << res;
}

```