#include <bits/stdc++.h>
using namespace std;
const int oo = 0x3f3f3f3f;
const long long OO = 3e12 + 10;
const int Mod = 1e9 + 7;
const int maxn = 1e5 + 5;
int dp[maxn];
int a[maxn];
vector<int> num[maxn];
void Init() {
  for (int i = 2; i < maxn; i++)
    for (int j = i; j < maxn; j += i) num[j].push_back(i);
}
int main() {
  Init();
  int n, ans, last;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  memset(dp, 0, sizeof dp);
  for (int i = 1; i <= n; i++) {
    int temp = 0;
    for (vector<int>::iterator it = num[a[i]].begin(); it != num[a[i]].end();
         it++)
      temp = max(temp, dp[*it]);
    for (vector<int>::iterator it = num[a[i]].begin(); it != num[a[i]].end();
         it++)
      dp[*it] = temp + 1;
  }
  ans = 1;
  for (int i = 0; i < maxn; i++) ans = max(dp[i], ans);
  printf("%d\n", ans);
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 oo = 0x3f3f3f3f;
const long long OO = 3e12 + 10;
const int Mod = 1e9 + 7;
const int maxn = 1e5 + 5;
int dp[maxn];
int a[maxn];
vector<int> num[maxn];
void Init() {
  for (int i = 2; i < maxn; i++)
    for (int j = i; j < maxn; j += i) num[j].push_back(i);
}
int main() {
  Init();
  int n, ans, last;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  memset(dp, 0, sizeof dp);
  for (int i = 1; i <= n; i++) {
    int temp = 0;
    for (vector<int>::iterator it = num[a[i]].begin(); it != num[a[i]].end();
         it++)
      temp = max(temp, dp[*it]);
    for (vector<int>::iterator it = num[a[i]].begin(); it != num[a[i]].end();
         it++)
      dp[*it] = temp + 1;
  }
  ans = 1;
  for (int i = 0; i < maxn; i++) ans = max(dp[i], ans);
  printf("%d\n", ans);
  return 0;
}

```