#include <bits/stdc++.h>
using namespace std;
vector<int> v[100000 + 5];
int dp[100000 + 5], num[100000 + 5];
void gcd(int x, int y) {
  if (x == 1) {
    return;
  }
  for (int i = 2; i < sqrt(x); i++) {
    if (x % i == 0) {
      v[y].push_back(x / i);
      v[y].push_back(i);
    }
  }
  if (((int)sqrt(x)) == sqrt(x)) {
    v[y].push_back(sqrt(x));
  }
  if (v[y].size() == 0) {
    v[y].push_back(x);
  }
  return;
}
int main() {
  int n, maxc;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> num[i];
    gcd(num[i], i);
  }
  memset(dp, 0, 100000 + 4);
  for (int i = 0; i < n; i++) {
    maxc = -1000;
    for (int j = 0; j < v[i].size(); j++) {
      dp[v[i][j]]++;
      maxc = max(maxc, dp[v[i][j]]);
    }
    for (int j = 0; j < v[i].size(); j++) {
      dp[v[i][j]] = maxc;
    }
  }
  int maxt = 1;
  for (int i = 0; i <= num[n - 1]; i++) {
    maxt = max(maxt, dp[i]);
  }
  cout << maxt;
}

### Prompt

Please create a solution in Cpp 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;
vector<int> v[100000 + 5];
int dp[100000 + 5], num[100000 + 5];
void gcd(int x, int y) {
  if (x == 1) {
    return;
  }
  for (int i = 2; i < sqrt(x); i++) {
    if (x % i == 0) {
      v[y].push_back(x / i);
      v[y].push_back(i);
    }
  }
  if (((int)sqrt(x)) == sqrt(x)) {
    v[y].push_back(sqrt(x));
  }
  if (v[y].size() == 0) {
    v[y].push_back(x);
  }
  return;
}
int main() {
  int n, maxc;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> num[i];
    gcd(num[i], i);
  }
  memset(dp, 0, 100000 + 4);
  for (int i = 0; i < n; i++) {
    maxc = -1000;
    for (int j = 0; j < v[i].size(); j++) {
      dp[v[i][j]]++;
      maxc = max(maxc, dp[v[i][j]]);
    }
    for (int j = 0; j < v[i].size(); j++) {
      dp[v[i][j]] = maxc;
    }
  }
  int maxt = 1;
  for (int i = 0; i <= num[n - 1]; i++) {
    maxt = max(maxt, dp[i]);
  }
  cout << maxt;
}

```