#include <bits/stdc++.h>
using namespace std;
inline long long get_num(char ch) {
  if (ch == '-')
    return 0;
  else if (ch >= 'a' && ch <= 'z') {
    return 1 + (ch - 'a');
  } else if (ch >= 'A' && ch <= 'Z') {
    return 27 + (ch - 'A');
  } else if (ch >= '0' && ch <= '9') {
    return 53 + (ch - '0');
  }
}
int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
inline int GA(long long n, vector<long long>& vec) {
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    vec.push_back(x);
  }
}
inline int GAEG(long long m, vector<long long> vec[]) {
  for (long long i = 0; i < m; ++i) {
    long long x, y;
    cin >> x >> y;
    x--, y--;
    vec[x].push_back(y);
    vec[y].push_back(x);
  }
}
long long arr[100001];
map<long long, long long> mp;
long long mx = 1;
int main() {
  long long n;
  cin >> n;
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    long long ff = sqrt(x);
    for (long long j = 1; j < ff + 1; ++j) {
      if (!(x % j)) {
        if (j != 1) arr[x] = max(arr[x], arr[mp[j]] + 1);
        arr[x] = max(arr[x], arr[mp[x / j]] + 1);
        mp[x / j] = x;
        mp[j] = x;
      }
    }
    mx = max(mx, arr[x]);
  }
  cout << mx << endl;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
inline long long get_num(char ch) {
  if (ch == '-')
    return 0;
  else if (ch >= 'a' && ch <= 'z') {
    return 1 + (ch - 'a');
  } else if (ch >= 'A' && ch <= 'Z') {
    return 27 + (ch - 'A');
  } else if (ch >= '0' && ch <= '9') {
    return 53 + (ch - '0');
  }
}
int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
inline int GA(long long n, vector<long long>& vec) {
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    vec.push_back(x);
  }
}
inline int GAEG(long long m, vector<long long> vec[]) {
  for (long long i = 0; i < m; ++i) {
    long long x, y;
    cin >> x >> y;
    x--, y--;
    vec[x].push_back(y);
    vec[y].push_back(x);
  }
}
long long arr[100001];
map<long long, long long> mp;
long long mx = 1;
int main() {
  long long n;
  cin >> n;
  for (long long i = 0; i < n; ++i) {
    long long x;
    cin >> x;
    long long ff = sqrt(x);
    for (long long j = 1; j < ff + 1; ++j) {
      if (!(x % j)) {
        if (j != 1) arr[x] = max(arr[x], arr[mp[j]] + 1);
        arr[x] = max(arr[x], arr[mp[x / j]] + 1);
        mp[x / j] = x;
        mp[j] = x;
      }
    }
    mx = max(mx, arr[x]);
  }
  cout << mx << endl;
}

```