#include <bits/stdc++.h>
using namespace std;
const int N = 3e5 + 9;
int n, mem[200001][3];
int arr[200000];
vector<int> sets[200000];
vector<int> ids[200000];
int solve(int i, bool took) {
  if (i == n) return 0;
  if (mem[i][took] != -1) return mem[i][took];
  int ret = 0;
  if (!took) ret = solve(i + 1, 0);
  for (int j = 0; j < sets[i].size(); j++) {
    int cur_set = sets[i][j];
    if (cur_set == 1) continue;
    int pos = lower_bound(ids[cur_set].begin(), ids[cur_set].end(), i) -
              ids[cur_set].begin();
    if (pos == ids[cur_set].size() - 1) continue;
    ret = max(ret, solve(ids[cur_set][pos + 1], 1) + 1);
  }
  return mem[i][took] = ret;
}
void get_sets(int i) {
  for (int j = 1; j * j <= arr[i]; j++)
    if (arr[i] % j == 0) {
      sets[i].push_back(j);
      ids[j].push_back(i);
      if (arr[i] / j != j)
        sets[i].push_back(arr[i] / j), ids[arr[i] / j].push_back(i);
    }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  memset(mem, -1, sizeof mem);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i], get_sets(i);
  cout << solve(0, 0) + 1 << '\n';
  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;
const int N = 3e5 + 9;
int n, mem[200001][3];
int arr[200000];
vector<int> sets[200000];
vector<int> ids[200000];
int solve(int i, bool took) {
  if (i == n) return 0;
  if (mem[i][took] != -1) return mem[i][took];
  int ret = 0;
  if (!took) ret = solve(i + 1, 0);
  for (int j = 0; j < sets[i].size(); j++) {
    int cur_set = sets[i][j];
    if (cur_set == 1) continue;
    int pos = lower_bound(ids[cur_set].begin(), ids[cur_set].end(), i) -
              ids[cur_set].begin();
    if (pos == ids[cur_set].size() - 1) continue;
    ret = max(ret, solve(ids[cur_set][pos + 1], 1) + 1);
  }
  return mem[i][took] = ret;
}
void get_sets(int i) {
  for (int j = 1; j * j <= arr[i]; j++)
    if (arr[i] % j == 0) {
      sets[i].push_back(j);
      ids[j].push_back(i);
      if (arr[i] / j != j)
        sets[i].push_back(arr[i] / j), ids[arr[i] / j].push_back(i);
    }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  memset(mem, -1, sizeof mem);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i], get_sets(i);
  cout << solve(0, 0) + 1 << '\n';
  return 0;
}

```