#include <bits/stdc++.h>
using namespace std;
const int MAX = 100005;
bool isprime[MAX];
int a[MAX];
int ans[100005];
vector<int> factor[MAX];
void get_prime() {
  memset(isprime, 1, sizeof(isprime));
  for (int i = 2; i < MAX; i++) {
    if (isprime[i]) {
      factor[i].push_back(i);
      for (int j = 2 * i; j < MAX; j += i) {
        factor[j].push_back(i);
        isprime[j] = 0;
      }
    }
  }
}
int main() {
  get_prime();
  int n;
  while (cin >> n) {
    memset(ans, 0, sizeof(ans));
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) {
      int m = 0;
      for (int j = 0; j < factor[a[i]].size(); j++)
        m = max(ans[factor[a[i]][j]] + 1, m);
      for (int j = 0; j < factor[a[i]].size(); j++) ans[factor[a[i]][j]] = m;
    }
    int M = 1;
    for (int i = 0; i < 10000; i++) M = max(M, ans[i]);
    cout << M << endl;
  }
  return 0;
}

### Prompt

Your challenge is to write 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;
const int MAX = 100005;
bool isprime[MAX];
int a[MAX];
int ans[100005];
vector<int> factor[MAX];
void get_prime() {
  memset(isprime, 1, sizeof(isprime));
  for (int i = 2; i < MAX; i++) {
    if (isprime[i]) {
      factor[i].push_back(i);
      for (int j = 2 * i; j < MAX; j += i) {
        factor[j].push_back(i);
        isprime[j] = 0;
      }
    }
  }
}
int main() {
  get_prime();
  int n;
  while (cin >> n) {
    memset(ans, 0, sizeof(ans));
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) {
      int m = 0;
      for (int j = 0; j < factor[a[i]].size(); j++)
        m = max(ans[factor[a[i]][j]] + 1, m);
      for (int j = 0; j < factor[a[i]].size(); j++) ans[factor[a[i]][j]] = m;
    }
    int M = 1;
    for (int i = 0; i < 10000; i++) M = max(M, ans[i]);
    cout << M << endl;
  }
  return 0;
}

```