#include <bits/stdc++.h>
int hash[1000006], a[1000006], pr[1000006], hash2[1000006], temp[1000006];
int main() {
  int i, n, j, c, max, k;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  for (i = 0; i < 100006; i++) hash[i] = 1;
  hash[0] = hash[1] = 0;
  c = 0;
  for (i = 2; i < 100006; i++) {
    if (hash[i] == 1) {
      pr[c++] = i;
      for (j = i; j < 100006; j = j + i) hash[j] = 0;
    }
  }
  for (i = 0; i < 100006; i++) hash2[i] = 0;
  for (i = 0; i < c; i++) hash2[pr[i]] = 1;
  for (i = 0; i < 100006; i++) hash[i] = 0;
  for (i = 0; i < n; i++) {
    if (hash2[a[i]] == 1 || a[i] == 1)
      hash[a[i]]++;
    else {
      j = 0;
      k = 0;
      while (pr[j] <= a[i] / 2) {
        if (a[i] % pr[j] == 0) temp[k++] = pr[j];
        j++;
      }
      max = 0;
      for (j = 0; j < k; j++) {
        if (max < hash[temp[j]]) max = hash[temp[j]];
      }
      for (j = 0; j < k; j++) {
        hash[temp[j]] = max + 1;
      }
    }
  }
  max = 0;
  for (i = 0; i < 100006; i++) {
    if (hash[i] > max) max = hash[i];
  }
  printf("%d", max);
  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>
int hash[1000006], a[1000006], pr[1000006], hash2[1000006], temp[1000006];
int main() {
  int i, n, j, c, max, k;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  for (i = 0; i < 100006; i++) hash[i] = 1;
  hash[0] = hash[1] = 0;
  c = 0;
  for (i = 2; i < 100006; i++) {
    if (hash[i] == 1) {
      pr[c++] = i;
      for (j = i; j < 100006; j = j + i) hash[j] = 0;
    }
  }
  for (i = 0; i < 100006; i++) hash2[i] = 0;
  for (i = 0; i < c; i++) hash2[pr[i]] = 1;
  for (i = 0; i < 100006; i++) hash[i] = 0;
  for (i = 0; i < n; i++) {
    if (hash2[a[i]] == 1 || a[i] == 1)
      hash[a[i]]++;
    else {
      j = 0;
      k = 0;
      while (pr[j] <= a[i] / 2) {
        if (a[i] % pr[j] == 0) temp[k++] = pr[j];
        j++;
      }
      max = 0;
      for (j = 0; j < k; j++) {
        if (max < hash[temp[j]]) max = hash[temp[j]];
      }
      for (j = 0; j < k; j++) {
        hash[temp[j]] = max + 1;
      }
    }
  }
  max = 0;
  for (i = 0; i < 100006; i++) {
    if (hash[i] > max) max = hash[i];
  }
  printf("%d", max);
  return 0;
}

```