#include <bits/stdc++.h>
using namespace std;
vector<int> nn[100011];
int maxn[100111] = {0};
int main() {
  int n;
  while (scanf("%d", &n) > 0) {
    int aa[100011] = {0};
    int res = 1;
    for (int i = 0; i < n; i++) {
      scanf("%d", &aa[i]);
      for (int j = 2; j * j <= aa[i]; j++) {
        if (aa[i] % j == 0) {
          nn[aa[i]].push_back(j);
          if (j * j != aa[i]) nn[aa[i]].push_back(aa[i] / j);
        }
      }
      nn[aa[i]].push_back(aa[i]);
    }
    for (int i = 0; i < nn[aa[0]].size(); i++) maxn[nn[aa[0]][i]] = 1;
    for (int i = 1; i < n; i++) {
      int maxx = 0;
      for (int j = 0; j < nn[aa[i]].size(); j++)
        if (maxn[nn[aa[i]][j]] > maxx) maxx = maxn[nn[aa[i]][j]];
      maxx++;
      if (maxx > res) res = maxx;
      for (int j = 0; j < nn[aa[i]].size(); j++)
        if (maxx > maxn[nn[aa[i]][j]]) maxn[nn[aa[i]][j]] = maxx;
    }
    printf("%d\n", res);
  }
  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;
vector<int> nn[100011];
int maxn[100111] = {0};
int main() {
  int n;
  while (scanf("%d", &n) > 0) {
    int aa[100011] = {0};
    int res = 1;
    for (int i = 0; i < n; i++) {
      scanf("%d", &aa[i]);
      for (int j = 2; j * j <= aa[i]; j++) {
        if (aa[i] % j == 0) {
          nn[aa[i]].push_back(j);
          if (j * j != aa[i]) nn[aa[i]].push_back(aa[i] / j);
        }
      }
      nn[aa[i]].push_back(aa[i]);
    }
    for (int i = 0; i < nn[aa[0]].size(); i++) maxn[nn[aa[0]][i]] = 1;
    for (int i = 1; i < n; i++) {
      int maxx = 0;
      for (int j = 0; j < nn[aa[i]].size(); j++)
        if (maxn[nn[aa[i]][j]] > maxx) maxx = maxn[nn[aa[i]][j]];
      maxx++;
      if (maxx > res) res = maxx;
      for (int j = 0; j < nn[aa[i]].size(); j++)
        if (maxx > maxn[nn[aa[i]][j]]) maxn[nn[aa[i]][j]] = maxx;
    }
    printf("%d\n", res);
  }
  return 0;
}

```