#include <bits/stdc++.h>
using namespace std;
int toInt(string s) {
  istringstream sin(s);
  int t;
  sin >> t;
  return t;
}
template <class T>
string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T>
void chmin(T &t, T f) {
  if (t > f) t = f;
}
template <class T>
void chmax(T &t, T f) {
  if (t < f) t = f;
}
int p[100010];
int dp[100010];
int len[100010];
int main() {
  int n;
  cin >> n;
  int a[100010];
  int i, j;
  for (i = (0); i < (n); i++) cin >> a[i];
  for (i = (0); i < (100010); i++) p[i] = 2000000007;
  p[1] = 1;
  for (i = (2); i < (100010); i++)
    if (p[i] == 2000000007) {
      for (j = i; j < 100010; j += i) p[j] = min(p[j], i);
    }
  for (i = (0); i < (n); i++) {
    int t = a[i];
    dp[i] = 1;
    while (t > 1) {
      int x = p[t];
      dp[i] = max(dp[i], len[x] + 1);
      while (t % x == 0) t /= x;
    }
    t = a[i];
    while (t > 1) {
      int x = p[t];
      len[x] = max(len[x], dp[i]);
      while (t % x == 0) t /= x;
    }
  }
  cout << *max_element(dp, dp + n) << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
int toInt(string s) {
  istringstream sin(s);
  int t;
  sin >> t;
  return t;
}
template <class T>
string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T>
void chmin(T &t, T f) {
  if (t > f) t = f;
}
template <class T>
void chmax(T &t, T f) {
  if (t < f) t = f;
}
int p[100010];
int dp[100010];
int len[100010];
int main() {
  int n;
  cin >> n;
  int a[100010];
  int i, j;
  for (i = (0); i < (n); i++) cin >> a[i];
  for (i = (0); i < (100010); i++) p[i] = 2000000007;
  p[1] = 1;
  for (i = (2); i < (100010); i++)
    if (p[i] == 2000000007) {
      for (j = i; j < 100010; j += i) p[j] = min(p[j], i);
    }
  for (i = (0); i < (n); i++) {
    int t = a[i];
    dp[i] = 1;
    while (t > 1) {
      int x = p[t];
      dp[i] = max(dp[i], len[x] + 1);
      while (t % x == 0) t /= x;
    }
    t = a[i];
    while (t > 1) {
      int x = p[t];
      len[x] = max(len[x], dp[i]);
      while (t % x == 0) t /= x;
    }
  }
  cout << *max_element(dp, dp + n) << endl;
  return 0;
}

```