#include <bits/stdc++.h>
using namespace std;
using namespace std;
long long powm(long long base, long long exp, long long mod = 1000000007) {
  long long ans = 1;
  while (exp) {
    if (exp & 1) ans = (ans * base) % mod;
    exp >>= 1, base = (base * base) % mod;
  }
  return ans;
}
long long maxp[100005], len[100005];
vector<long long> factors;
int main() {
  long long n, x, ans = 0, curr = 0, flag = 0;
  maxp[1] = 1;
  for (long long i = 2; i < 100005; i++)
    if (maxp[i] == 0) {
      for (long long j = 2 * i; j < 100005; j += i) maxp[j] = i;
      maxp[i] = i;
    }
  cin >> n;
  for (long long i = 1; i < n + 1; i++) {
    cin >> x, curr = 0, factors.clear();
    flag |= (x != 1);
    while (1) {
      if (x == 1 or maxp[x] == 1) break;
      long long tmp = maxp[x];
      factors.push_back(tmp);
      while (x % tmp == 0) x /= tmp;
    }
    for (auto i : factors) curr = max(curr, ++len[i]);
    for (auto i : factors) len[i] = curr;
  }
  for (long long i = 0; i < 100005; i++) ans = max(ans, len[i]);
  if (!flag)
    cout << 1;
  else
    cout << ans;
  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;
using namespace std;
long long powm(long long base, long long exp, long long mod = 1000000007) {
  long long ans = 1;
  while (exp) {
    if (exp & 1) ans = (ans * base) % mod;
    exp >>= 1, base = (base * base) % mod;
  }
  return ans;
}
long long maxp[100005], len[100005];
vector<long long> factors;
int main() {
  long long n, x, ans = 0, curr = 0, flag = 0;
  maxp[1] = 1;
  for (long long i = 2; i < 100005; i++)
    if (maxp[i] == 0) {
      for (long long j = 2 * i; j < 100005; j += i) maxp[j] = i;
      maxp[i] = i;
    }
  cin >> n;
  for (long long i = 1; i < n + 1; i++) {
    cin >> x, curr = 0, factors.clear();
    flag |= (x != 1);
    while (1) {
      if (x == 1 or maxp[x] == 1) break;
      long long tmp = maxp[x];
      factors.push_back(tmp);
      while (x % tmp == 0) x /= tmp;
    }
    for (auto i : factors) curr = max(curr, ++len[i]);
    for (auto i : factors) len[i] = curr;
  }
  for (long long i = 0; i < 100005; i++) ans = max(ans, len[i]);
  if (!flag)
    cout << 1;
  else
    cout << ans;
  return 0;
}

```