#include <bits/stdc++.h>
using namespace std;
int M, a[2000000], n, ans;
int d[2000000];
int DP(int v, int x) {
  M = 0;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) M = max(M, d[i]);
    while (x % i == 0) x /= i;
  }
  if (x != 1) M = max(M, d[x]);
  x = v;
  M++;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) d[i] = M;
    while (x % i == 0) x /= i;
  }
  if (x != 1) d[x] = M;
  return M;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) ans = max(ans, DP(a[i], a[i]));
  printf("%d", ans);
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
int M, a[2000000], n, ans;
int d[2000000];
int DP(int v, int x) {
  M = 0;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) M = max(M, d[i]);
    while (x % i == 0) x /= i;
  }
  if (x != 1) M = max(M, d[x]);
  x = v;
  M++;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) d[i] = M;
    while (x % i == 0) x /= i;
  }
  if (x != 1) d[x] = M;
  return M;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) ans = max(ans, DP(a[i], a[i]));
  printf("%d", ans);
  return 0;
}

```