#include <bits/stdc++.h>
using namespace std;
const int MX = 1e5 + 1;
int n, a[MX], dp[MX], p[MX];
void init() {
  for (int i = 0; i < MX; i++) p[i] = 0;
  p[0] = p[1] = 0;
  for (int i = 2; i < MX; i++) {
    if (p[i] == 0) {
      p[i] = i;
      for (int j = 2 * i; j < MX; j += i)
        if (p[j] == 0) p[j] = i;
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  init();
  for (int i = 0; i < MX; i++) dp[i] = 0;
  for (int i = 0; i < n; i++) {
    if (p[a[i]] == a[i] || a[i] == 1) {
      dp[a[i]] = 1;
      continue;
    }
    int c = a[i], mx = 0;
    vector<int> cur;
    while (c > 1) {
      int pr = p[c];
      mx = max(mx, dp[pr]);
      cur.push_back(pr);
      while (c % pr == 0) {
        c /= pr;
      }
    }
    for (int j = 0; j < cur.size(); j++) {
      dp[cur[j]] = mx + 1;
    }
  }
  int ans = 0;
  for (int i = 0; i < MX; i++) {
    ans = max(ans, dp[i]);
  }
  printf("%d", ans);
  return 0;
}

### Prompt

Your challenge is to write 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;
const int MX = 1e5 + 1;
int n, a[MX], dp[MX], p[MX];
void init() {
  for (int i = 0; i < MX; i++) p[i] = 0;
  p[0] = p[1] = 0;
  for (int i = 2; i < MX; i++) {
    if (p[i] == 0) {
      p[i] = i;
      for (int j = 2 * i; j < MX; j += i)
        if (p[j] == 0) p[j] = i;
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  init();
  for (int i = 0; i < MX; i++) dp[i] = 0;
  for (int i = 0; i < n; i++) {
    if (p[a[i]] == a[i] || a[i] == 1) {
      dp[a[i]] = 1;
      continue;
    }
    int c = a[i], mx = 0;
    vector<int> cur;
    while (c > 1) {
      int pr = p[c];
      mx = max(mx, dp[pr]);
      cur.push_back(pr);
      while (c % pr == 0) {
        c /= pr;
      }
    }
    for (int j = 0; j < cur.size(); j++) {
      dp[cur[j]] = mx + 1;
    }
  }
  int ans = 0;
  for (int i = 0; i < MX; i++) {
    ans = max(ans, dp[i]);
  }
  printf("%d", ans);
  return 0;
}

```