#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:60000000")
using namespace std;
template <class T>
T sqr(T x) {
  return x * x;
}
double const pi = 3.1415926535897932384626433832795;
int const inf = (int)1e9;
long long const inf64 = (long long)4e18;
const string name = "b";
const int NMAX = 100100;
int n, a[NMAX], ans[NMAX], PREV[NMAX];
int main() {
  cin >> n;
  for (int i = 0; i < (int)n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < (int)NMAX; i++) PREV[i] = -1;
  int answer = 0;
  for (int i = 0; i < (int)n; i++) {
    ans[i] = 1;
    for (int d = 2; d * d <= a[i]; ++d)
      if (a[i] % d == 0) {
        if (PREV[d] >= 0) ans[i] = max(ans[i], ans[PREV[d]] + 1);
        if (PREV[a[i] / d] >= 0) ans[i] = max(ans[i], ans[PREV[a[i] / d]] + 1);
        PREV[d] = PREV[a[i] / d] = i;
      }
    PREV[a[i]] = i;
    answer = max(answer, ans[i]);
  }
  cout << answer << endl;
  return 0;
}

### Prompt

Please create a solution in CPP 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>
#pragma comment(linker, "/STACK:60000000")
using namespace std;
template <class T>
T sqr(T x) {
  return x * x;
}
double const pi = 3.1415926535897932384626433832795;
int const inf = (int)1e9;
long long const inf64 = (long long)4e18;
const string name = "b";
const int NMAX = 100100;
int n, a[NMAX], ans[NMAX], PREV[NMAX];
int main() {
  cin >> n;
  for (int i = 0; i < (int)n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < (int)NMAX; i++) PREV[i] = -1;
  int answer = 0;
  for (int i = 0; i < (int)n; i++) {
    ans[i] = 1;
    for (int d = 2; d * d <= a[i]; ++d)
      if (a[i] % d == 0) {
        if (PREV[d] >= 0) ans[i] = max(ans[i], ans[PREV[d]] + 1);
        if (PREV[a[i] / d] >= 0) ans[i] = max(ans[i], ans[PREV[a[i] / d]] + 1);
        PREV[d] = PREV[a[i] / d] = i;
      }
    PREV[a[i]] = i;
    answer = max(answer, ans[i]);
  }
  cout << answer << endl;
  return 0;
}

```