#include <bits/stdc++.h>
using namespace std;
bool z[100010] = {0};
int zz[10000];
int f[10000] = {0};
int all = 0;
void prework() {
  for (int i = 2; i <= 100000; i++) {
    if (z[i]) continue;
    for (int k = i + i; k <= 100000; k += i) z[k] = true;
  }
  for (int i = 2; i <= 100000; i++)
    if (!z[i]) {
      all++;
      zz[all] = i;
    }
}
int main() {
  prework();
  int N, now, ANS = 1;
  scanf("%d", &N);
  for (int i = 1; i <= N; i++) {
    int ans = 0;
    scanf("%d", &now);
    vector<int> v;
    for (int ii = 1; ii <= all; ii++) {
      if (now < zz[ii]) break;
      if (now % zz[ii] == 0) {
        v.push_back(ii);
        ans = max(ans, f[ii]);
        while (now % zz[ii] == 0) now /= zz[ii];
      }
    }
    ans++;
    for (vector<int>::iterator k = v.begin(); k != v.end(); k++) f[*k] = ans;
    if (ans > ANS) ANS = ans;
  }
  cout << ANS << endl;
}

### 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;
bool z[100010] = {0};
int zz[10000];
int f[10000] = {0};
int all = 0;
void prework() {
  for (int i = 2; i <= 100000; i++) {
    if (z[i]) continue;
    for (int k = i + i; k <= 100000; k += i) z[k] = true;
  }
  for (int i = 2; i <= 100000; i++)
    if (!z[i]) {
      all++;
      zz[all] = i;
    }
}
int main() {
  prework();
  int N, now, ANS = 1;
  scanf("%d", &N);
  for (int i = 1; i <= N; i++) {
    int ans = 0;
    scanf("%d", &now);
    vector<int> v;
    for (int ii = 1; ii <= all; ii++) {
      if (now < zz[ii]) break;
      if (now % zz[ii] == 0) {
        v.push_back(ii);
        ans = max(ans, f[ii]);
        while (now % zz[ii] == 0) now /= zz[ii];
      }
    }
    ans++;
    for (vector<int>::iterator k = v.begin(); k != v.end(); k++) f[*k] = ans;
    if (ans > ANS) ANS = ans;
  }
  cout << ANS << endl;
}

```