#include <bits/stdc++.h>
using namespace std;
const int INF = 1000000000;
const int MAXN = 100005;
const int MAXV = 1000010;
inline long long gcd(long long n1, long long n2) {
  return n2 == 0 ? abs(n1) : gcd(n2, n1 % n2);
}
int v[MAXN];
int w[MAXN];
int aux[50];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  while (cin >> n) {
    for (int i = 0; i < n; ++i) cin >> v[i];
    memset(w, 0, sizeof w);
    for (int i = 0; i < n; ++i) {
      int t = 0, x = v[i];
      for (int j = 2; j * j <= x; j++) {
        if (x % j) continue;
        aux[t++] = j;
        while (x % j == 0) x /= j;
      }
      if (x != 1) aux[t++] = x;
      int melhor = 0;
      for (int j = 0; j < t; ++j) melhor = max(melhor, w[aux[j]]);
      for (int j = 0; j < t; ++j) w[aux[j]] = melhor + 1;
    }
    int ans = 1;
    for (int i = 0; i < MAXN; ++i) ans = max(ans, w[i]);
    cout << ans << endl;
  }
}

### 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 INF = 1000000000;
const int MAXN = 100005;
const int MAXV = 1000010;
inline long long gcd(long long n1, long long n2) {
  return n2 == 0 ? abs(n1) : gcd(n2, n1 % n2);
}
int v[MAXN];
int w[MAXN];
int aux[50];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  while (cin >> n) {
    for (int i = 0; i < n; ++i) cin >> v[i];
    memset(w, 0, sizeof w);
    for (int i = 0; i < n; ++i) {
      int t = 0, x = v[i];
      for (int j = 2; j * j <= x; j++) {
        if (x % j) continue;
        aux[t++] = j;
        while (x % j == 0) x /= j;
      }
      if (x != 1) aux[t++] = x;
      int melhor = 0;
      for (int j = 0; j < t; ++j) melhor = max(melhor, w[aux[j]]);
      for (int j = 0; j < t; ++j) w[aux[j]] = melhor + 1;
    }
    int ans = 1;
    for (int i = 0; i < MAXN; ++i) ans = max(ans, w[i]);
    cout << ans << endl;
  }
}

```