#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
int n, f[N], as = 1, a[N];
inline int read() {
  register char ch = getchar();
  register int x = 0;
  register bool y = 1;
  while (ch != '-' && (ch > '9' || ch < '0')) ch = getchar();
  if (ch == '-') ch = getchar(), y = 0;
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (ch ^ '0'), ch = getchar();
  return y ? x : -x;
}
int main() {
  n = read();
  while (n--) {
    int x = read(), mx = f[x];
    for (register int i = 2; i * i <= x; i++)
      if (x % i == 0) mx = max(max(mx, f[i]), f[x / i]);
    for (register int i = 2; i * i <= x; i++)
      if (x % i == 0) f[i] = f[x / i] = mx + 1;
    f[x] = mx + 1;
    as = max(as, mx + 1);
  }
  printf("%d\n", as);
  return 0;
}

### Prompt

Create a solution in CPP for 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 = 100005;
int n, f[N], as = 1, a[N];
inline int read() {
  register char ch = getchar();
  register int x = 0;
  register bool y = 1;
  while (ch != '-' && (ch > '9' || ch < '0')) ch = getchar();
  if (ch == '-') ch = getchar(), y = 0;
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (ch ^ '0'), ch = getchar();
  return y ? x : -x;
}
int main() {
  n = read();
  while (n--) {
    int x = read(), mx = f[x];
    for (register int i = 2; i * i <= x; i++)
      if (x % i == 0) mx = max(max(mx, f[i]), f[x / i]);
    for (register int i = 2; i * i <= x; i++)
      if (x % i == 0) f[i] = f[x / i] = mx + 1;
    f[x] = mx + 1;
    as = max(as, mx + 1);
  }
  printf("%d\n", as);
  return 0;
}

```