#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
int sieve[maxn], dp[maxn];
void init() {
  memset(sieve, 1, sizeof(sieve));
  sieve[0] = sieve[1] = 0;
  for (int i = 2; i < maxn; i++)
    if (sieve[i])
      for (int j = 2 * i; j < maxn; j += i) sieve[j] = 0;
}
int main() {
  init();
  vector<int> prime;
  int n, ans = 0;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    vector<int> p;
    if (sieve[a[i]]) p.push_back(a[i]);
    for (int j = 2; j * j <= a[i]; j++)
      if (a[i] % j == 0) {
        if (sieve[j]) p.push_back(j);
        if (j * j != a[i] and sieve[a[i] / j]) p.push_back(a[i] / j);
      }
    int tmp = 0;
    for (int j = 0; j < (int)p.size(); j++) tmp = max(tmp, dp[p[j]]);
    for (int j = 0; j < (int)p.size(); j++) dp[p[j]] = tmp + 1;
  }
  for (int i = 0; i < maxn; i++) ans = max(ans, dp[i]);
  cout << max(ans, 1);
  return 0;
}

### Prompt

In CPP, your task is to solve 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 int maxn = 1e5 + 5;
int sieve[maxn], dp[maxn];
void init() {
  memset(sieve, 1, sizeof(sieve));
  sieve[0] = sieve[1] = 0;
  for (int i = 2; i < maxn; i++)
    if (sieve[i])
      for (int j = 2 * i; j < maxn; j += i) sieve[j] = 0;
}
int main() {
  init();
  vector<int> prime;
  int n, ans = 0;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    vector<int> p;
    if (sieve[a[i]]) p.push_back(a[i]);
    for (int j = 2; j * j <= a[i]; j++)
      if (a[i] % j == 0) {
        if (sieve[j]) p.push_back(j);
        if (j * j != a[i] and sieve[a[i] / j]) p.push_back(a[i] / j);
      }
    int tmp = 0;
    for (int j = 0; j < (int)p.size(); j++) tmp = max(tmp, dp[p[j]]);
    for (int j = 0; j < (int)p.size(); j++) dp[p[j]] = tmp + 1;
  }
  for (int i = 0; i < maxn; i++) ans = max(ans, dp[i]);
  cout << max(ans, 1);
  return 0;
}

```