#include <bits/stdc++.h>
using namespace std;
const long long int N = 100005;
const long long int mod = 1e9 + 7;
map<long long int, long long int> cnt;
long long int dp[N], a[N], ans = 0;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  long long int i, j, k;
  for (i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    a[i] = x;
    dp[a[i]] = 1;
    vector<long long int> v;
    for (j = 2; j * j <= x; j++) {
      if (x % j == 0) {
        v.push_back(j);
        if (j != x / j) v.push_back(x / j);
      }
    }
    for (auto x : v) dp[a[i]] = max(dp[a[i]], dp[x] + 1);
    for (auto x : v) dp[x] = dp[a[i]];
    ans = max(ans, dp[a[i]]);
  }
  cout << ans;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 int N = 100005;
const long long int mod = 1e9 + 7;
map<long long int, long long int> cnt;
long long int dp[N], a[N], ans = 0;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  long long int i, j, k;
  for (i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    a[i] = x;
    dp[a[i]] = 1;
    vector<long long int> v;
    for (j = 2; j * j <= x; j++) {
      if (x % j == 0) {
        v.push_back(j);
        if (j != x / j) v.push_back(x / j);
      }
    }
    for (auto x : v) dp[a[i]] = max(dp[a[i]], dp[x] + 1);
    for (auto x : v) dp[x] = dp[a[i]];
    ans = max(ans, dp[a[i]]);
  }
  cout << ans;
}

```