#include <bits/stdc++.h>
using namespace std;
int arr[100005], mark[100005], prime[100005], ans[100005];
vector<int> adj[100005];
int main() {
  int n, i, j, val, cur;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &arr[i]);
    mark[arr[i]]++;
  }
  for (i = 0; i < 100005; i++) {
    ans[i] = 0;
    prime[i] = 0;
  }
  for (i = 2; i < 100005; i++) {
    if (prime[i] == 0) {
      cur = i;
      for (j = i; j < 100005; j += i) {
        prime[j] = cur;
        if (mark[j] != 0) {
          adj[j].push_back(cur);
          cur = j;
        }
      }
    }
  }
  int maxi = 1;
  for (i = 1; i <= n; i++) {
    val = -1;
    for (j = 0; j < adj[arr[i]].size(); j++) {
      val = max(val, ans[adj[arr[i]][j]]);
    }
    ans[arr[i]] = 1 + val;
    maxi = max(maxi, ans[arr[i]]);
  }
  printf("%d\n", maxi);
  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;
int arr[100005], mark[100005], prime[100005], ans[100005];
vector<int> adj[100005];
int main() {
  int n, i, j, val, cur;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &arr[i]);
    mark[arr[i]]++;
  }
  for (i = 0; i < 100005; i++) {
    ans[i] = 0;
    prime[i] = 0;
  }
  for (i = 2; i < 100005; i++) {
    if (prime[i] == 0) {
      cur = i;
      for (j = i; j < 100005; j += i) {
        prime[j] = cur;
        if (mark[j] != 0) {
          adj[j].push_back(cur);
          cur = j;
        }
      }
    }
  }
  int maxi = 1;
  for (i = 1; i <= n; i++) {
    val = -1;
    for (j = 0; j < adj[arr[i]].size(); j++) {
      val = max(val, ans[adj[arr[i]][j]]);
    }
    ans[arr[i]] = 1 + val;
    maxi = max(maxi, ans[arr[i]]);
  }
  printf("%d\n", maxi);
  return 0;
}

```