#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 998244353;
const long long int N = 200005;
long long int siv[N], dp[N] = {0};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n, i, j;
  for (i = 0; i < N; i++) siv[i] = i;
  for (i = 2; i * i < N; i++) {
    if (siv[i] == i) {
      for (j = i * i; j < N; j += i) {
        if (siv[j] == j) siv[j] = i;
      }
    }
  }
  cin >> n;
  long long int a[n + 5];
  for (i = 0; i < n; i++) cin >> a[i];
  long long int mx;
  for (i = 0; i < n; i++) {
    mx = 0;
    long long int te = a[i];
    set<long long int> s;
    while (te != 1) {
      mx = max(dp[siv[te]], mx);
      s.insert(siv[te]);
      te /= siv[te];
    }
    for (auto it = s.begin(); it != s.end(); it++) dp[*it] = mx + 1;
  }
  sort(dp, dp + N);
  cout << max(1ll, dp[N - 1]);
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 long long int MOD = 998244353;
const long long int N = 200005;
long long int siv[N], dp[N] = {0};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n, i, j;
  for (i = 0; i < N; i++) siv[i] = i;
  for (i = 2; i * i < N; i++) {
    if (siv[i] == i) {
      for (j = i * i; j < N; j += i) {
        if (siv[j] == j) siv[j] = i;
      }
    }
  }
  cin >> n;
  long long int a[n + 5];
  for (i = 0; i < n; i++) cin >> a[i];
  long long int mx;
  for (i = 0; i < n; i++) {
    mx = 0;
    long long int te = a[i];
    set<long long int> s;
    while (te != 1) {
      mx = max(dp[siv[te]], mx);
      s.insert(siv[te]);
      te /= siv[te];
    }
    for (auto it = s.begin(); it != s.end(); it++) dp[*it] = mx + 1;
  }
  sort(dp, dp + N);
  cout << max(1ll, dp[N - 1]);
  return 0;
}

```