#include <bits/stdc++.h>
using namespace std;
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
const int N = 1e5 + 10;
int a[N], n;
int main() {
  scanf("%d", &n);
  if (n == 1) return puts("1") * 0;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    vector<int> v;
    for (int i = 2; i * i <= x; i++) {
      if (x % i == 0) {
        v.push_back(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) v.push_back(x);
    int mx = 0;
    for (int i : v) mx = max(mx, a[i]);
    mx++;
    for (auto i : v) a[i] = mx;
  }
  int mx = 0;
  for (int i = 2; i < N; i++) mx = max(mx, a[i]);
  printf("%d\n", mx);
  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;
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
const int N = 1e5 + 10;
int a[N], n;
int main() {
  scanf("%d", &n);
  if (n == 1) return puts("1") * 0;
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    vector<int> v;
    for (int i = 2; i * i <= x; i++) {
      if (x % i == 0) {
        v.push_back(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) v.push_back(x);
    int mx = 0;
    for (int i : v) mx = max(mx, a[i]);
    mx++;
    for (auto i : v) a[i] = mx;
  }
  int mx = 0;
  for (int i = 2; i < N; i++) mx = max(mx, a[i]);
  printf("%d\n", mx);
  return 0;
}

```