#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
const int SQRTN = 320;
const int LOGN = 20;
int n, a[N], dp[N];
vector<int> f;
int mx[N];
vector<int> prime;
bool notPrime[N];
void seive() {
  notPrime[1] = 1;
  for (int i = 2; i < N; i++)
    if (!notPrime[i]) {
      for (int j = i + i; j < N; j += i) notPrime[j] = 1;
      prime.push_back(i);
    }
}
void get(int a) {
  f.clear();
  for (int i = 2; i * i <= a; i++) {
    if (a % i) continue;
    f.push_back(i);
    while (a % i == 0) a /= i;
  }
  if (a != 1) f.push_back(a);
}
void add(int idx) {
  for (int i = 0; i < f.size(); i++) mx[f[i]] = max(mx[f[i]], dp[idx]);
}
int mxx = 0;
int main() {
  scanf("%d", &n);
  seive();
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  for (int i = 0; i < n; i++) {
    dp[i] = 1;
    get(a[i]);
    for (int j = 0; j < f.size(); j++) dp[i] = max(dp[i], mx[f[j]] + 1);
    mxx = max(mxx, dp[i]);
    add(i);
  }
  cout << mxx << endl;
}

### 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 int N = 2e5 + 10;
const int SQRTN = 320;
const int LOGN = 20;
int n, a[N], dp[N];
vector<int> f;
int mx[N];
vector<int> prime;
bool notPrime[N];
void seive() {
  notPrime[1] = 1;
  for (int i = 2; i < N; i++)
    if (!notPrime[i]) {
      for (int j = i + i; j < N; j += i) notPrime[j] = 1;
      prime.push_back(i);
    }
}
void get(int a) {
  f.clear();
  for (int i = 2; i * i <= a; i++) {
    if (a % i) continue;
    f.push_back(i);
    while (a % i == 0) a /= i;
  }
  if (a != 1) f.push_back(a);
}
void add(int idx) {
  for (int i = 0; i < f.size(); i++) mx[f[i]] = max(mx[f[i]], dp[idx]);
}
int mxx = 0;
int main() {
  scanf("%d", &n);
  seive();
  for (int i = 0; i < n; i++) scanf("%d", a + i);
  for (int i = 0; i < n; i++) {
    dp[i] = 1;
    get(a[i]);
    for (int j = 0; j < f.size(); j++) dp[i] = max(dp[i], mx[f[j]] + 1);
    mxx = max(mxx, dp[i]);
    add(i);
  }
  cout << mxx << endl;
}

```