#include <bits/stdc++.h>
using namespace std;
int notprime[1000001];
vector<int> fac[1000001];
void sieve() {
  int test, i, j, x = 1, n;
  for (i = 2; i < 100001; i++) {
    if (!notprime[i]) {
      fac[i].push_back(i);
      for (j = i * 2; j < 100002; j += i) {
        notprime[j] = 1;
        fac[j].push_back(i);
      }
    }
  }
}
int dp[100001];
int main() {
  int i, j, n, t, c = 65, k;
  sieve();
  vector<int> q;
  scanf("%d", &n);
  for (int i = (int)0; i < (int)n; ++i) {
    scanf("%d", &j);
    q.push_back(j);
  }
  int ans = 0, final = 0;
  for (int i = (int)0; i < (int)n; ++i) {
    t = int(fac[q[i]].size());
    ans = 0;
    for (int j = (int)0; j < (int)t; ++j)
      ans = ((ans) > (dp[fac[q[i]][j]]) ? (ans) : (dp[fac[q[i]][j]]));
    ans++;
    for (int j = (int)0; j < (int)t; ++j) dp[fac[q[i]][j]] = ans;
    final = ((ans) > (final) ? (ans) : (final));
  }
  printf("%d\n", final);
  return 0;
}

### 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;
int notprime[1000001];
vector<int> fac[1000001];
void sieve() {
  int test, i, j, x = 1, n;
  for (i = 2; i < 100001; i++) {
    if (!notprime[i]) {
      fac[i].push_back(i);
      for (j = i * 2; j < 100002; j += i) {
        notprime[j] = 1;
        fac[j].push_back(i);
      }
    }
  }
}
int dp[100001];
int main() {
  int i, j, n, t, c = 65, k;
  sieve();
  vector<int> q;
  scanf("%d", &n);
  for (int i = (int)0; i < (int)n; ++i) {
    scanf("%d", &j);
    q.push_back(j);
  }
  int ans = 0, final = 0;
  for (int i = (int)0; i < (int)n; ++i) {
    t = int(fac[q[i]].size());
    ans = 0;
    for (int j = (int)0; j < (int)t; ++j)
      ans = ((ans) > (dp[fac[q[i]][j]]) ? (ans) : (dp[fac[q[i]][j]]));
    ans++;
    for (int j = (int)0; j < (int)t; ++j) dp[fac[q[i]][j]] = ans;
    final = ((ans) > (final) ? (ans) : (final));
  }
  printf("%d\n", final);
  return 0;
}

```