#include <bits/stdc++.h>
using namespace std;
const int MXN = 101616;
vector<int> mlfe[MXN];
int dp[MXN];
void input();
int n;
void qarbal(int f) {
  for (int i = 2; i <= f; i++)
    if (mlfe[i].empty()) {
      mlfe[i].push_back(i);
      for (int j = 0; j * i <= f; j++) mlfe[i * j].push_back(i);
    }
}
int mx_mlfe(int v) {
  int mx = 0;
  for (int i = 0; i < int(mlfe[v].size()); i++) mx = max(mx, dp[mlfe[v][i]]);
  return mx;
}
int main() {
  fill(dp, dp + MXN, 0);
  for (int i = 0; i < MXN; i++) mlfe[i].reserve(16);
  qarbal(MXN - 100);
  cin >> n;
  while (n--) {
    int a;
    cin >> a;
    int p = mx_mlfe(a) + 1;
    for (int i = 0; i < int(mlfe[a].size()); i++) dp[mlfe[a][i]] = p;
  }
  cout << max(1, *max_element(dp, dp + MXN));
  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;
const int MXN = 101616;
vector<int> mlfe[MXN];
int dp[MXN];
void input();
int n;
void qarbal(int f) {
  for (int i = 2; i <= f; i++)
    if (mlfe[i].empty()) {
      mlfe[i].push_back(i);
      for (int j = 0; j * i <= f; j++) mlfe[i * j].push_back(i);
    }
}
int mx_mlfe(int v) {
  int mx = 0;
  for (int i = 0; i < int(mlfe[v].size()); i++) mx = max(mx, dp[mlfe[v][i]]);
  return mx;
}
int main() {
  fill(dp, dp + MXN, 0);
  for (int i = 0; i < MXN; i++) mlfe[i].reserve(16);
  qarbal(MXN - 100);
  cin >> n;
  while (n--) {
    int a;
    cin >> a;
    int p = mx_mlfe(a) + 1;
    for (int i = 0; i < int(mlfe[a].size()); i++) dp[mlfe[a][i]] = p;
  }
  cout << max(1, *max_element(dp, dp + MXN));
  return 0;
}

```