265_D. Good Sequences_6386
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.
#include <bits/stdc++.h>
using namespace std;
const int N = 100002;
int a[N];
int d[N];
int main() {
  int n, m, i, j;
  cin >> n;
  for (i = 1; i <= n; i++) cin >> a[i];
  int ans = 0;
  for (i = 1; i <= n; i++) {
    int cnt = 0;
    for (j = 2; j * j <= a[i]; j++) {
      if (a[i] % j == 0) {
        cnt = max(cnt, d[j]);
        cnt = max(cnt, d[a[i] / j]);
      }
    }
    for (j = 2; j * j <= a[i]; j++) {
      if (a[i] % j == 0) {
        d[j] = max(d[j], cnt + 1);
        d[a[i] / j] = max(d[a[i] / j], cnt + 1);
      }
    }
    d[a[i]] = max(d[a[i]], cnt + 1);
    ans = max(cnt + 1, ans);
  }
  cout << ans;
}
