#include <bits/stdc++.h>
using namespace std;
int n, a[100010], sang[100010] = {0}, f[100010] = {0}, g[100010] = {0};
vector<int> u[100010];
void taosang() {
  for (int i = 2; i <= 100000; ++i)
    if (sang[i] == 0)
      for (int j = i + i; j <= 100000; j += i) sang[j] = i;
}
void process() {
  int t, ans = -1, x, m;
  for (int(i) = (1); (i) <= (n); ++i) {
    t = 0;
    m = 0;
    x = a[i];
    while (sang[x] > 0) {
      if (u[i].empty() || sang[x] != u[i].back()) {
        u[i].push_back(sang[x]);
        m++;
      }
      x /= sang[x];
    }
    if (x > 0 && (u[i].empty() || x != u[i].back())) {
      u[i].push_back(x);
      m++;
    }
    for (int(j) = 0; (j) < (m); ++(j))
      if (g[u[i][j]] > t) t = g[u[i][j]];
    for (int(j) = 0; (j) < (m); ++(j))
      if (t + 1 > g[u[i][j]]) g[u[i][j]] = t + 1;
    if (t + 1 > ans) ans = t + 1;
  }
  cout << ans;
}
int main(void) {
  scanf("%d", &n);
  for (int(i) = (1); (i) <= (n); ++i) scanf("%d", &a[i]);
  taosang();
  process();
  return 0;
}

### Prompt

Please formulate a cpp solution 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>
using namespace std;
int n, a[100010], sang[100010] = {0}, f[100010] = {0}, g[100010] = {0};
vector<int> u[100010];
void taosang() {
  for (int i = 2; i <= 100000; ++i)
    if (sang[i] == 0)
      for (int j = i + i; j <= 100000; j += i) sang[j] = i;
}
void process() {
  int t, ans = -1, x, m;
  for (int(i) = (1); (i) <= (n); ++i) {
    t = 0;
    m = 0;
    x = a[i];
    while (sang[x] > 0) {
      if (u[i].empty() || sang[x] != u[i].back()) {
        u[i].push_back(sang[x]);
        m++;
      }
      x /= sang[x];
    }
    if (x > 0 && (u[i].empty() || x != u[i].back())) {
      u[i].push_back(x);
      m++;
    }
    for (int(j) = 0; (j) < (m); ++(j))
      if (g[u[i][j]] > t) t = g[u[i][j]];
    for (int(j) = 0; (j) < (m); ++(j))
      if (t + 1 > g[u[i][j]]) g[u[i][j]] = t + 1;
    if (t + 1 > ans) ans = t + 1;
  }
  cout << ans;
}
int main(void) {
  scanf("%d", &n);
  for (int(i) = (1); (i) <= (n); ++i) scanf("%d", &a[i]);
  taosang();
  process();
  return 0;
}

```