#include <bits/stdc++.h>
using namespace std;
const int maxN = 100000;
vector<int> divs[maxN + 1];
void fillDivs() {
  bool isPrime[maxN + 1];
  for (int i = 0; i <= maxN; i++) isPrime[i] = true;
  for (int i = 2; i <= maxN; i++)
    if (isPrime[i]) {
      divs[i].push_back(i);
      for (int j = 2 * i; j <= maxN; j += i) {
        isPrime[j] = false;
        divs[j].push_back(i);
      }
    }
}
int main() {
  int n;
  cin >> n;
  vector<int> v(n);
  fillDivs();
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v.begin(), v.end());
  int longestPaths[maxN + 1];
  for (int i = 0; i <= maxN; i++) longestPaths[i] = -1;
  int maxBestWay = -1;
  for (int i = 0; i < n; i++) {
    int x = v[i];
    int bestWay = 1;
    for (int j = 0; j < divs[x].size(); j++)
      bestWay = max(bestWay, 1 + longestPaths[divs[x][j]]);
    for (int j = 0; j < divs[x].size(); j++) longestPaths[divs[x][j]] = bestWay;
    maxBestWay = max(maxBestWay, bestWay);
  }
  cout << maxBestWay;
}

### 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 maxN = 100000;
vector<int> divs[maxN + 1];
void fillDivs() {
  bool isPrime[maxN + 1];
  for (int i = 0; i <= maxN; i++) isPrime[i] = true;
  for (int i = 2; i <= maxN; i++)
    if (isPrime[i]) {
      divs[i].push_back(i);
      for (int j = 2 * i; j <= maxN; j += i) {
        isPrime[j] = false;
        divs[j].push_back(i);
      }
    }
}
int main() {
  int n;
  cin >> n;
  vector<int> v(n);
  fillDivs();
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v.begin(), v.end());
  int longestPaths[maxN + 1];
  for (int i = 0; i <= maxN; i++) longestPaths[i] = -1;
  int maxBestWay = -1;
  for (int i = 0; i < n; i++) {
    int x = v[i];
    int bestWay = 1;
    for (int j = 0; j < divs[x].size(); j++)
      bestWay = max(bestWay, 1 + longestPaths[divs[x][j]]);
    for (int j = 0; j < divs[x].size(); j++) longestPaths[divs[x][j]] = bestWay;
    maxBestWay = max(maxBestWay, bestWay);
  }
  cout << maxBestWay;
}

```