#include <bits/stdc++.h>
void fileio_in_out() {
  freopen(".in", "r", stdin);
  freopen(".out", "w", stdout);
}
void fileio_txt() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
int m, n, k, nump = 0, ans = 0;
int a[1111111], b[1111111], f[1111111];
int main() {
  int i, j, l;
  memset(b, 0, sizeof(b));
  memset(f, 0, sizeof(f));
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (i = 1; i <= n; i++) {
    for (j = 1; j * j <= a[i]; j++)
      if (a[i] % j == 0) {
        f[i] =
            (((f[i]) > (f[b[a[i] / j]] + 1)) ? (f[i]) : (f[b[a[i] / j]] + 1));
        if (j > 1) f[i] = (((f[i]) > (f[b[j]] + 1)) ? (f[i]) : (f[b[j]] + 1));
        ans = (((ans) > (f[i])) ? (ans) : (f[i]));
        b[j] = b[a[i] / j] = i;
      }
  }
  printf("%d\n", ans);
  return 0;
}

### Prompt

Generate 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>
void fileio_in_out() {
  freopen(".in", "r", stdin);
  freopen(".out", "w", stdout);
}
void fileio_txt() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
int m, n, k, nump = 0, ans = 0;
int a[1111111], b[1111111], f[1111111];
int main() {
  int i, j, l;
  memset(b, 0, sizeof(b));
  memset(f, 0, sizeof(f));
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (i = 1; i <= n; i++) {
    for (j = 1; j * j <= a[i]; j++)
      if (a[i] % j == 0) {
        f[i] =
            (((f[i]) > (f[b[a[i] / j]] + 1)) ? (f[i]) : (f[b[a[i] / j]] + 1));
        if (j > 1) f[i] = (((f[i]) > (f[b[j]] + 1)) ? (f[i]) : (f[b[j]] + 1));
        ans = (((ans) > (f[i])) ? (ans) : (f[i]));
        b[j] = b[a[i] / j] = i;
      }
  }
  printf("%d\n", ans);
  return 0;
}

```