#include <bits/stdc++.h>
using namespace std;
const double EPS = (1e-7);
int dcmp(double x, double y) { return fabs(x - y) <= EPS ? 0 : x < y ? -1 : 1; }
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return (a * (b / gcd(a, b))); }
int dp[100001], a[100001];
void solution() {
  int n;
  scanf("%d", &(n));
  for (int i = 0; i < int(n); i++) scanf("%d", &(a[i]));
  memset(dp, 0, sizeof(dp));
  ;
  for (int i = 0; i < int(n); i++) {
    int x = a[i], mx = 1;
    for (int j = 2; j * j <= x; j++) {
      if (x % j == 0) {
        mx = max(mx, dp[j] + 1);
        mx = max(mx, dp[x / j] + 1);
      }
    }
    dp[x] = max(dp[x], mx);
    for (int j = 1; j * j <= x; j++) {
      if (x % j == 0) {
        dp[j] = max(dp[j], mx);
        dp[x / j] = max(dp[x / j], mx);
      }
    }
  }
  cout << *max_element(dp, dp + 100001);
}
int main() {
  double beg = clock();
  ios::sync_with_stdio(false);
  solution();
  return 0;
}

### Prompt

Create a solution in CPP for 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 double EPS = (1e-7);
int dcmp(double x, double y) { return fabs(x - y) <= EPS ? 0 : x < y ? -1 : 1; }
long long gcd(long long a, long long b) { return (b == 0 ? a : gcd(b, a % b)); }
long long lcm(long long a, long long b) { return (a * (b / gcd(a, b))); }
int dp[100001], a[100001];
void solution() {
  int n;
  scanf("%d", &(n));
  for (int i = 0; i < int(n); i++) scanf("%d", &(a[i]));
  memset(dp, 0, sizeof(dp));
  ;
  for (int i = 0; i < int(n); i++) {
    int x = a[i], mx = 1;
    for (int j = 2; j * j <= x; j++) {
      if (x % j == 0) {
        mx = max(mx, dp[j] + 1);
        mx = max(mx, dp[x / j] + 1);
      }
    }
    dp[x] = max(dp[x], mx);
    for (int j = 1; j * j <= x; j++) {
      if (x % j == 0) {
        dp[j] = max(dp[j], mx);
        dp[x / j] = max(dp[x / j], mx);
      }
    }
  }
  cout << *max_element(dp, dp + 100001);
}
int main() {
  double beg = clock();
  ios::sync_with_stdio(false);
  solution();
  return 0;
}

```