#include <bits/stdc++.h>
using namespace std;
int32_t dx[] = {2, 2, -2, -2, 1, 1, -1, -1};
int32_t dy[] = {1, -1, 1, -1, 2, -2, 2, -2};
vector<long long> fac(100005, -1);
void init() {
  fac[1] = 1;
  for (long long i = 2; i < 100005; i++) {
    if (fac[i] != -1) continue;
    fac[i] = i;
    for (long long j = i * i; j < 100005; j += i) {
      if (fac[j] != -1) continue;
      fac[j] = i;
    }
  }
}
int32_t main() {
  init();
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> arr(n);
  for (long long i = 0; i < n; ++i) cin >> arr[i];
  vector<long long> count(100005, 0);
  long long answer = 1;
  for (long long i = 0; i < n; ++i) {
    long long temp = arr[i];
    long long maxChainLength = 0;
    while (temp != 1) {
      long long curr = fac[temp];
      maxChainLength = max(maxChainLength, count[curr]);
      while (fac[temp] == curr) {
        temp /= fac[temp];
      }
    }
    answer = max(answer, 1 + maxChainLength);
    temp = arr[i];
    while (temp != 1) {
      long long curr = fac[temp];
      count[curr] = max(count[curr], 1 + maxChainLength);
      while (fac[temp] == curr) {
        temp /= fac[temp];
      }
    }
  }
  cout << answer << endl;
}

### Prompt

Please formulate a cpp solution to 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;
int32_t dx[] = {2, 2, -2, -2, 1, 1, -1, -1};
int32_t dy[] = {1, -1, 1, -1, 2, -2, 2, -2};
vector<long long> fac(100005, -1);
void init() {
  fac[1] = 1;
  for (long long i = 2; i < 100005; i++) {
    if (fac[i] != -1) continue;
    fac[i] = i;
    for (long long j = i * i; j < 100005; j += i) {
      if (fac[j] != -1) continue;
      fac[j] = i;
    }
  }
}
int32_t main() {
  init();
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  vector<long long> arr(n);
  for (long long i = 0; i < n; ++i) cin >> arr[i];
  vector<long long> count(100005, 0);
  long long answer = 1;
  for (long long i = 0; i < n; ++i) {
    long long temp = arr[i];
    long long maxChainLength = 0;
    while (temp != 1) {
      long long curr = fac[temp];
      maxChainLength = max(maxChainLength, count[curr]);
      while (fac[temp] == curr) {
        temp /= fac[temp];
      }
    }
    answer = max(answer, 1 + maxChainLength);
    temp = arr[i];
    while (temp != 1) {
      long long curr = fac[temp];
      count[curr] = max(count[curr], 1 + maxChainLength);
      while (fac[temp] == curr) {
        temp /= fac[temp];
      }
    }
  }
  cout << answer << endl;
}

```