#include <bits/stdc++.h>
using namespace std;
long long int dp[100100];
int main() {
  long long int n, i, j, ans = -1;
  cin >> n;
  long long int arr[n];
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) {
    vector<long long int> v;
    long long int mx = -1;
    map<long long int, long long int> mpp;
    long long int x = arr[i];
    for (j = 2; j * j <= arr[i]; j++) {
      while (x % j == 0) {
        if (mpp[j] == 0) {
          mx = max(mx, dp[j] + 1);
          v.push_back(j);
          mpp[j] = 1;
        }
        x /= j;
      }
    }
    if (x != 1) {
      if (mpp[x] == 0) {
        mpp[x] = 1;
        mx = max(mx, dp[x] + 1);
        v.push_back(x);
      }
    }
    for (j = 0; j < v.size(); j++) dp[v[j]] = mx;
    ans = max(ans, mx);
  }
  if (n == 1)
    cout << 1;
  else
    cout << ans;
  return 0;
}

### Prompt

Please formulate 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>
using namespace std;
long long int dp[100100];
int main() {
  long long int n, i, j, ans = -1;
  cin >> n;
  long long int arr[n];
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) {
    vector<long long int> v;
    long long int mx = -1;
    map<long long int, long long int> mpp;
    long long int x = arr[i];
    for (j = 2; j * j <= arr[i]; j++) {
      while (x % j == 0) {
        if (mpp[j] == 0) {
          mx = max(mx, dp[j] + 1);
          v.push_back(j);
          mpp[j] = 1;
        }
        x /= j;
      }
    }
    if (x != 1) {
      if (mpp[x] == 0) {
        mpp[x] = 1;
        mx = max(mx, dp[x] + 1);
        v.push_back(x);
      }
    }
    for (j = 0; j < v.size(); j++) dp[v[j]] = mx;
    ans = max(ans, mx);
  }
  if (n == 1)
    cout << 1;
  else
    cout << ans;
  return 0;
}

```