#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 50;
int arr[maxn];
vector<int> D[maxn];
bool mark[maxn];
int ans[maxn];
int dp[maxn];
int32_t main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
  }
  for (int i = 2; i < (maxn >> 1) + 5; i++) {
    if (mark[i] == 0) {
      for (int j = i; j < maxn; j += i) {
        D[j].push_back(i);
        mark[j] = 1;
      }
    }
  }
  for (int i = 0; i < D[arr[0]].size(); i++) {
    ans[D[arr[0]][i]] = 1;
  }
  int A, mx;
  for (int i = 1; i < n; i++) {
    mx = 0;
    A = arr[i];
    for (int j : D[A]) {
      mx = max(mx, ans[j]);
    }
    for (int j : D[A]) {
      ans[j] = mx + 1;
    }
    dp[A] = mx + 1;
  }
  int ans1 = 0;
  for (int i = 0; i < maxn; i++) {
    ans1 = max(ans1, dp[i]);
  }
  if (n == 1) ans1 = 1;
  printf("%d", ans1);
  return 0;
}

### 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;
const int maxn = 1e5 + 50;
int arr[maxn];
vector<int> D[maxn];
bool mark[maxn];
int ans[maxn];
int dp[maxn];
int32_t main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
  }
  for (int i = 2; i < (maxn >> 1) + 5; i++) {
    if (mark[i] == 0) {
      for (int j = i; j < maxn; j += i) {
        D[j].push_back(i);
        mark[j] = 1;
      }
    }
  }
  for (int i = 0; i < D[arr[0]].size(); i++) {
    ans[D[arr[0]][i]] = 1;
  }
  int A, mx;
  for (int i = 1; i < n; i++) {
    mx = 0;
    A = arr[i];
    for (int j : D[A]) {
      mx = max(mx, ans[j]);
    }
    for (int j : D[A]) {
      ans[j] = mx + 1;
    }
    dp[A] = mx + 1;
  }
  int ans1 = 0;
  for (int i = 0; i < maxn; i++) {
    ans1 = max(ans1, dp[i]);
  }
  if (n == 1) ans1 = 1;
  printf("%d", ans1);
  return 0;
}

```