#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
int lst[N];
set<int> pre[N];
bool p[N];
void sieve() {
  p[0] = p[1] = true;
  for (int i = 2; i * i < N; i++) {
    if (!p[i]) {
      for (int j = i * i; j < N; j += i) {
        p[j] = true;
      }
    }
  }
  for (int i = 0; i < N; i++) {
    lst[i] = 1;
  }
  for (int i = 2; i < N; i++) {
    if (!p[i]) {
      for (int j = i; j < N; j += i) {
        lst[j] = i;
      }
    }
  }
}
int main() {
  sieve();
  int n, res = 1;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    int temp = x, mx = 0;
    while (lst[temp] > 1) {
      int t = lst[temp];
      while (t == lst[temp]) {
        temp /= t;
      }
      if (pre[t].size() == 0) {
        pre[t].insert(0);
      }
      if (pre[t].size()) {
        mx = max(mx, *(--pre[t].end()) + 1);
      }
    }
    temp = x;
    while (lst[temp] > 1) {
      int t = lst[temp];
      while (t == lst[temp]) {
        temp /= t;
      }
      pre[t].insert(mx);
    }
    res = max(res, mx);
  }
  printf("%d", res);
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 = 100005;
int lst[N];
set<int> pre[N];
bool p[N];
void sieve() {
  p[0] = p[1] = true;
  for (int i = 2; i * i < N; i++) {
    if (!p[i]) {
      for (int j = i * i; j < N; j += i) {
        p[j] = true;
      }
    }
  }
  for (int i = 0; i < N; i++) {
    lst[i] = 1;
  }
  for (int i = 2; i < N; i++) {
    if (!p[i]) {
      for (int j = i; j < N; j += i) {
        lst[j] = i;
      }
    }
  }
}
int main() {
  sieve();
  int n, res = 1;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    int temp = x, mx = 0;
    while (lst[temp] > 1) {
      int t = lst[temp];
      while (t == lst[temp]) {
        temp /= t;
      }
      if (pre[t].size() == 0) {
        pre[t].insert(0);
      }
      if (pre[t].size()) {
        mx = max(mx, *(--pre[t].end()) + 1);
      }
    }
    temp = x;
    while (lst[temp] > 1) {
      int t = lst[temp];
      while (t == lst[temp]) {
        temp /= t;
      }
      pre[t].insert(mx);
    }
    res = max(res, mx);
  }
  printf("%d", res);
  return 0;
}

```