#include <bits/stdc++.h>
using namespace std;
int a[100500];
int len[100500];
int d[100500];
int n;
void fct(vector<int> &r, int x) {
  r.clear();
  int imax = min((int)sqrt(1.0 * x) + 2, x);
  for (int i = 2; x > 1; i++) {
    if (imax == i) {
      r.push_back(x);
      return;
    }
    if (0 == x % i) {
      r.push_back(i);
      do {
        x /= i;
      } while (0 == x % i);
    }
  }
}
int main() {
  scanf("%d", &n);
  if (1 == n) {
    puts("1");
    return 0;
  }
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  vector<int> r;
  for (int i = 0; i < n; i++) {
    fct(r, a[i]);
    int dmax = 0;
    for (int j = 0; j < (int)r.size(); j++) {
      len[i] = max(len[i], d[r[j]] + 1);
      dmax = max(d[r[j]] + 1, dmax);
    }
    for (int j = 0; j < (int)r.size(); j++) d[r[j]] = dmax;
  }
  int res = 0;
  for (int i = 0; i < n; i++) res = max(res, len[i]);
  cout << res;
  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;
int a[100500];
int len[100500];
int d[100500];
int n;
void fct(vector<int> &r, int x) {
  r.clear();
  int imax = min((int)sqrt(1.0 * x) + 2, x);
  for (int i = 2; x > 1; i++) {
    if (imax == i) {
      r.push_back(x);
      return;
    }
    if (0 == x % i) {
      r.push_back(i);
      do {
        x /= i;
      } while (0 == x % i);
    }
  }
}
int main() {
  scanf("%d", &n);
  if (1 == n) {
    puts("1");
    return 0;
  }
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  vector<int> r;
  for (int i = 0; i < n; i++) {
    fct(r, a[i]);
    int dmax = 0;
    for (int j = 0; j < (int)r.size(); j++) {
      len[i] = max(len[i], d[r[j]] + 1);
      dmax = max(d[r[j]] + 1, dmax);
    }
    for (int j = 0; j < (int)r.size(); j++) d[r[j]] = dmax;
  }
  int res = 0;
  for (int i = 0; i < n; i++) res = max(res, len[i]);
  cout << res;
  return 0;
}

```