#include <bits/stdc++.h>
using namespace std;
const long long N = 2e5 + 30, Mod = 1e9 + 7;
const long long SQ = 330;
int dp[N], spf[N], dp2[N], a[N];
vector<int> pr2[N], pr[N];
int M[N];
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  for (int i = 0; i < N; i++) spf[i] = i;
  for (int i = 2; i < N; i++)
    if (spf[i] == i)
      for (int j = i * 2; j < N; j += i) spf[j] = min(spf[j], i);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    int x = a[i];
    while (x > 1) {
      int cur = spf[x];
      while (x % cur == 0) x /= cur;
      pr[a[i]].push_back(cur);
      pr2[cur].push_back(a[i]);
    }
  }
  int ans = 1;
  for (int i = 1; i <= n; i++) {
    int res = 0;
    for (auto u : pr[a[i]]) res = max(res, dp2[u]);
    dp[a[i]] = res + 1;
    for (auto u : pr[a[i]]) dp2[u] = max(dp2[u], dp[a[i]]);
    ans = max(ans, dp[a[i]]);
  }
  for (int i = 1; i <= 10; i++) {
  }
  cout << ans;
  return (0);
}

### Prompt

Generate 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 long long N = 2e5 + 30, Mod = 1e9 + 7;
const long long SQ = 330;
int dp[N], spf[N], dp2[N], a[N];
vector<int> pr2[N], pr[N];
int M[N];
int main() {
  ios::sync_with_stdio(0), cin.tie(0);
  for (int i = 0; i < N; i++) spf[i] = i;
  for (int i = 2; i < N; i++)
    if (spf[i] == i)
      for (int j = i * 2; j < N; j += i) spf[j] = min(spf[j], i);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    int x = a[i];
    while (x > 1) {
      int cur = spf[x];
      while (x % cur == 0) x /= cur;
      pr[a[i]].push_back(cur);
      pr2[cur].push_back(a[i]);
    }
  }
  int ans = 1;
  for (int i = 1; i <= n; i++) {
    int res = 0;
    for (auto u : pr[a[i]]) res = max(res, dp2[u]);
    dp[a[i]] = res + 1;
    for (auto u : pr[a[i]]) dp2[u] = max(dp2[u], dp[a[i]]);
    ans = max(ans, dp[a[i]]);
  }
  for (int i = 1; i <= 10; i++) {
  }
  cout << ans;
  return (0);
}

```