#include <bits/stdc++.h>
using namespace std;
int dirx[] = {-1, -1, -1, 0, 0, 1, 1, 1};
int diry[] = {-1, 0, 1, -1, 1, -1, 0, 1};
int n;
const int N = 1e5 + 8;
int ar[N];
int main() {
  cin >> n;
  int mm = 0;
  for (long long i = 0; i < n; i++) {
    int scan;
    cin >> scan;
    mm = max(mm, scan);
    if (scan == 1) continue;
    int fac = 2;
    vector<int> prime;
    while (scan > 1 && fac * fac <= scan) {
      if (scan % fac == 0) {
        prime.push_back(fac);
        while (scan % fac == 0) {
          scan /= fac;
        }
      }
      fac++;
    }
    if (scan != 1) prime.push_back(scan);
    int mx = 0;
    for (long long j = 0; j < prime.size(); j++) mx = max(mx, ar[prime[j]]);
    for (auto j : prime) ar[j] = mx + 1;
  }
  int ans = 1;
  for (long long i = 0; i < mm + 1; i++) ans = max(ans, ar[i]);
  cout << ans;
}

### Prompt

In CPP, your task is to solve 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 dirx[] = {-1, -1, -1, 0, 0, 1, 1, 1};
int diry[] = {-1, 0, 1, -1, 1, -1, 0, 1};
int n;
const int N = 1e5 + 8;
int ar[N];
int main() {
  cin >> n;
  int mm = 0;
  for (long long i = 0; i < n; i++) {
    int scan;
    cin >> scan;
    mm = max(mm, scan);
    if (scan == 1) continue;
    int fac = 2;
    vector<int> prime;
    while (scan > 1 && fac * fac <= scan) {
      if (scan % fac == 0) {
        prime.push_back(fac);
        while (scan % fac == 0) {
          scan /= fac;
        }
      }
      fac++;
    }
    if (scan != 1) prime.push_back(scan);
    int mx = 0;
    for (long long j = 0; j < prime.size(); j++) mx = max(mx, ar[prime[j]]);
    for (auto j : prime) ar[j] = mx + 1;
  }
  int ans = 1;
  for (long long i = 0; i < mm + 1; i++) ans = max(ans, ar[i]);
  cout << ans;
}

```