#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
void solve() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int& i : v) cin >> i;
  vector<vector<int>> div(n);
  for (int i = 0; i < n; ++i) {
    for (int j = 2; j * j <= v[i]; ++j) {
      if (v[i] % j == 0) {
        div[i].push_back(j);
        if (v[i] / j != j) {
          div[i].push_back(v[i] / j);
        }
      }
    }
  }
  vector<int> dp(100001);
  for (int i = 0; i < n; ++i) {
    if (div[i].empty()) {
      dp[v[i]] = 1;
      continue;
    }
    for (int j : div[i]) {
      int t = v[i] - j;
      while (dp[t] == 0 && t > 0) t -= j;
      dp[v[i]] = max(dp[v[i]], dp[t] + 1);
    }
  }
  cout << *max_element(dp.begin(), dp.end()) << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tt = 1;
  while (tt--) {
    solve();
  }
}

### 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;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
void solve() {
  int n;
  cin >> n;
  vector<int> v(n);
  for (int& i : v) cin >> i;
  vector<vector<int>> div(n);
  for (int i = 0; i < n; ++i) {
    for (int j = 2; j * j <= v[i]; ++j) {
      if (v[i] % j == 0) {
        div[i].push_back(j);
        if (v[i] / j != j) {
          div[i].push_back(v[i] / j);
        }
      }
    }
  }
  vector<int> dp(100001);
  for (int i = 0; i < n; ++i) {
    if (div[i].empty()) {
      dp[v[i]] = 1;
      continue;
    }
    for (int j : div[i]) {
      int t = v[i] - j;
      while (dp[t] == 0 && t > 0) t -= j;
      dp[v[i]] = max(dp[v[i]], dp[t] + 1);
    }
  }
  cout << *max_element(dp.begin(), dp.end()) << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tt = 1;
  while (tt--) {
    solve();
  }
}

```