#include <bits/stdc++.h>
using namespace std;
long Max[100001], Num[100001];
long N;
void in() {
  scanf("%ld", &N);
  for (long i = 0; i < N; i++) scanf("%ld", &Num[i]);
}
void solve() {
  bool found;
  long maximum, maxLength = 0;
  for (long i = 0; i < N; i++) {
    maximum = 1;
    for (long n = 2; n < 317; n++)
      if (Num[i] % n == 0) {
        maximum = max(maximum, Max[n] + 1);
        maximum = n < Num[i] ? max(maximum, Max[Num[i] / n] + 1) : maximum;
      }
    for (long n = 1; n < 317; n++)
      if (Num[i] % n == 0) Max[n] = Max[Num[i] / n] = maximum;
    maxLength = max(maxLength, maximum);
  }
  printf("%ld\n", maxLength);
}
int main() {
  in();
  solve();
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;
long Max[100001], Num[100001];
long N;
void in() {
  scanf("%ld", &N);
  for (long i = 0; i < N; i++) scanf("%ld", &Num[i]);
}
void solve() {
  bool found;
  long maximum, maxLength = 0;
  for (long i = 0; i < N; i++) {
    maximum = 1;
    for (long n = 2; n < 317; n++)
      if (Num[i] % n == 0) {
        maximum = max(maximum, Max[n] + 1);
        maximum = n < Num[i] ? max(maximum, Max[Num[i] / n] + 1) : maximum;
      }
    for (long n = 1; n < 317; n++)
      if (Num[i] % n == 0) Max[n] = Max[Num[i] / n] = maximum;
    maxLength = max(maxLength, maximum);
  }
  printf("%ld\n", maxLength);
}
int main() {
  in();
  solve();
  return 0;
}

```