#include <bits/stdc++.h>
using namespace std;
const int MAX = 100001;
int pp[MAX];
int lst[MAX];
bool take[MAX];
int main() {
  ifstream fin("IO.txt");
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    pp[i] = 0;
    lst[i] = 0;
  }
  int x;
  int seq = 0;
  int cSeq = 0;
  while (n-- > 0) {
    cin >> x;
    lst[x] = x;
    pp[x]++;
    cSeq = 1;
    for (int i = 2; i * i <= x; i++)
      if (x % i == 0) {
        if (lst[i] < x) {
          pp[i] = max(pp[i] + 1, cSeq);
          lst[i] = x;
        }
        if (lst[x / i] < x) {
          pp[x / i] = max(pp[x / i] + 1, cSeq);
          lst[x / i] = x;
        }
        cSeq = max(cSeq, max(pp[i], pp[x / i]));
        seq = max(seq, cSeq);
      }
    for (int i = 2; i * i <= x; i++)
      if (x % i == 0) pp[i] = pp[x / i] = cSeq;
    seq = max(seq, cSeq);
  }
  cout << seq;
}

### Prompt

Your challenge is to write 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 MAX = 100001;
int pp[MAX];
int lst[MAX];
bool take[MAX];
int main() {
  ifstream fin("IO.txt");
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    pp[i] = 0;
    lst[i] = 0;
  }
  int x;
  int seq = 0;
  int cSeq = 0;
  while (n-- > 0) {
    cin >> x;
    lst[x] = x;
    pp[x]++;
    cSeq = 1;
    for (int i = 2; i * i <= x; i++)
      if (x % i == 0) {
        if (lst[i] < x) {
          pp[i] = max(pp[i] + 1, cSeq);
          lst[i] = x;
        }
        if (lst[x / i] < x) {
          pp[x / i] = max(pp[x / i] + 1, cSeq);
          lst[x / i] = x;
        }
        cSeq = max(cSeq, max(pp[i], pp[x / i]));
        seq = max(seq, cSeq);
      }
    for (int i = 2; i * i <= x; i++)
      if (x % i == 0) pp[i] = pp[x / i] = cSeq;
    seq = max(seq, cSeq);
  }
  cout << seq;
}

```