#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
int ar[maxn];
int factors[maxn];
int sp[maxn];
void pre() {
  for (int i = 2; i < maxn; i++)
    if (!sp[i]) {
      sp[i] = i;
      for (long long j = 1LL * i * i; j < maxn; j += i) {
        sp[j] = i;
      }
    }
}
unordered_set<int> factorize(int n) {
  unordered_set<int> ret;
  while (n != 1) {
    ret.insert(sp[n]);
    if (sp[n] == 0) break;
    n /= sp[n];
  }
  return ret;
}
int main() {
  int n;
  scanf("%d", &n);
  pre();
  for (int i = 0; i < n; ++i) scanf("%d", &ar[i]);
  for (int i = n - 1; i >= 0; i--) {
    unordered_set<int> facs = factorize(ar[i]);
    int curans = -1;
    for (int x : facs) {
      curans = max(curans, factors[x] + 1);
    }
    for (int x : facs) factors[x] = curans;
  }
  int ans = 0;
  for (int i = 0; i < maxn; i++) ans = max(ans, factors[i]);
  cout << max(ans, 1) << "\n";
}

### Prompt

Develop a solution in cpp 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 int maxn = 1e5 + 5;
int ar[maxn];
int factors[maxn];
int sp[maxn];
void pre() {
  for (int i = 2; i < maxn; i++)
    if (!sp[i]) {
      sp[i] = i;
      for (long long j = 1LL * i * i; j < maxn; j += i) {
        sp[j] = i;
      }
    }
}
unordered_set<int> factorize(int n) {
  unordered_set<int> ret;
  while (n != 1) {
    ret.insert(sp[n]);
    if (sp[n] == 0) break;
    n /= sp[n];
  }
  return ret;
}
int main() {
  int n;
  scanf("%d", &n);
  pre();
  for (int i = 0; i < n; ++i) scanf("%d", &ar[i]);
  for (int i = n - 1; i >= 0; i--) {
    unordered_set<int> facs = factorize(ar[i]);
    int curans = -1;
    for (int x : facs) {
      curans = max(curans, factors[x] + 1);
    }
    for (int x : facs) factors[x] = curans;
  }
  int ans = 0;
  for (int i = 0; i < maxn; i++) ans = max(ans, factors[i]);
  cout << max(ans, 1) << "\n";
}

```