#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const string LN = "\n";
const double eps = 1e-9;
const double pi = acos(-1.0);
const int INF = (int)2e9 + 7;
const long long LINF = (long long)9e18 + 7;
bool insert(int k, int x1, int x2) { return (k >= x1 && k <= x2); }
const int MAXN = 60007;
const int P1 = 239017;
const int P2 = 353251;
const long long MOD = 1e9 + 7;
const long long MOD2 = 1e9 + 9;
const bool is_testing = 0;
int n;
int dp[100007], a[100007], ma[100007];
int main() {
  if (is_testing) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  int ans = 1;
  for (int i = 0; i < n; i++) {
    dp[i] = 1;
    int del = 2;
    int cop = a[i];
    while (del * del <= cop) {
      while (cop % del == 0) {
        dp[i] = max(ma[del] + 1, dp[i]);
        cop /= del;
      }
      del++;
    }
    if (cop > 1) dp[i] = max(ma[cop] + 1, dp[i]);
    del = 2;
    while (del * del <= a[i]) {
      while (a[i] % del == 0) {
        ma[del] = max(ma[del], dp[i]);
        a[i] /= del;
      }
      del++;
    }
    if (a[i] > 1) ma[a[i]] = max(ma[a[i]], dp[i]);
    ans = max(ans, dp[i]);
  }
  cout << ans;
}

### 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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const string LN = "\n";
const double eps = 1e-9;
const double pi = acos(-1.0);
const int INF = (int)2e9 + 7;
const long long LINF = (long long)9e18 + 7;
bool insert(int k, int x1, int x2) { return (k >= x1 && k <= x2); }
const int MAXN = 60007;
const int P1 = 239017;
const int P2 = 353251;
const long long MOD = 1e9 + 7;
const long long MOD2 = 1e9 + 9;
const bool is_testing = 0;
int n;
int dp[100007], a[100007], ma[100007];
int main() {
  if (is_testing) {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  int ans = 1;
  for (int i = 0; i < n; i++) {
    dp[i] = 1;
    int del = 2;
    int cop = a[i];
    while (del * del <= cop) {
      while (cop % del == 0) {
        dp[i] = max(ma[del] + 1, dp[i]);
        cop /= del;
      }
      del++;
    }
    if (cop > 1) dp[i] = max(ma[cop] + 1, dp[i]);
    del = 2;
    while (del * del <= a[i]) {
      while (a[i] % del == 0) {
        ma[del] = max(ma[del], dp[i]);
        a[i] /= del;
      }
      del++;
    }
    if (a[i] > 1) ma[a[i]] = max(ma[a[i]], dp[i]);
    ans = max(ans, dp[i]);
  }
  cout << ans;
}

```