#include <bits/stdc++.h>
using namespace std;
int big_prime[100009], ans[100009];
int main() {
  for (int i = 2; i <= 100002; i++) {
    if (big_prime[i] == 0)
      for (int j = i; j < 100003; j += i) big_prime[j] = i;
  }
  int n, use, seed, len_sofar;
  scanf(" %d", &n);
  for (int qq = 0; qq < n; qq++) {
    scanf(" %d", &seed);
    len_sofar = 0;
    use = seed;
    while (use > 1) {
      int prime = big_prime[use];
      if (ans[prime] > len_sofar) len_sofar = ans[prime];
      use = use / prime;
    }
    use = seed;
    while (use > 1) {
      int prime = big_prime[use];
      ans[prime] = len_sofar + 1;
      use = use / prime;
    }
  }
  int ret = 1;
  for (int i = 0; i < 100003; i++) ret = max(ret, ans[i]);
  printf("%d\n", ret);
  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;
int big_prime[100009], ans[100009];
int main() {
  for (int i = 2; i <= 100002; i++) {
    if (big_prime[i] == 0)
      for (int j = i; j < 100003; j += i) big_prime[j] = i;
  }
  int n, use, seed, len_sofar;
  scanf(" %d", &n);
  for (int qq = 0; qq < n; qq++) {
    scanf(" %d", &seed);
    len_sofar = 0;
    use = seed;
    while (use > 1) {
      int prime = big_prime[use];
      if (ans[prime] > len_sofar) len_sofar = ans[prime];
      use = use / prime;
    }
    use = seed;
    while (use > 1) {
      int prime = big_prime[use];
      ans[prime] = len_sofar + 1;
      use = use / prime;
    }
  }
  int ret = 1;
  for (int i = 0; i < 100003; i++) ret = max(ret, ans[i]);
  printf("%d\n", ret);
  return 0;
}

```