#include <bits/stdc++.h>
int n, max, data[100020];
void input() {
  scanf("%d", &n);
  int i;
  for (i = 0; i < n; i++) {
    scanf("%d", &data[i]);
    if (max < data[i]) max = data[i];
  }
}
int prime[100020];
void findPrime() {
  int i, j;
  for (i = 2; i <= max; i++) {
    if (prime[i] == 0) {
      for (j = i * 2; j <= max; j += i) {
        if (prime[j] == 0) prime[j] = i;
      }
    }
  }
}
int res, dp[100020];
void solve() {
  int i, now, m;
  for (i = 0; i < n; i++) {
    now = data[i];
    m = 0;
    while (prime[now]) {
      if (dp[prime[now]] > m) m = dp[prime[now]];
      now = now / prime[now];
    }
    if (dp[now] > m) m = dp[now];
    if (res < m + 1) res = m + 1;
    now = data[i];
    while (prime[now]) {
      dp[prime[now]] = m + 1;
      now = now / prime[now];
    }
    dp[now] = m + 1;
  }
}
int main() {
  input();
  findPrime();
  solve();
  printf("%d\n", res);
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 n, max, data[100020];
void input() {
  scanf("%d", &n);
  int i;
  for (i = 0; i < n; i++) {
    scanf("%d", &data[i]);
    if (max < data[i]) max = data[i];
  }
}
int prime[100020];
void findPrime() {
  int i, j;
  for (i = 2; i <= max; i++) {
    if (prime[i] == 0) {
      for (j = i * 2; j <= max; j += i) {
        if (prime[j] == 0) prime[j] = i;
      }
    }
  }
}
int res, dp[100020];
void solve() {
  int i, now, m;
  for (i = 0; i < n; i++) {
    now = data[i];
    m = 0;
    while (prime[now]) {
      if (dp[prime[now]] > m) m = dp[prime[now]];
      now = now / prime[now];
    }
    if (dp[now] > m) m = dp[now];
    if (res < m + 1) res = m + 1;
    now = data[i];
    while (prime[now]) {
      dp[prime[now]] = m + 1;
      now = now / prime[now];
    }
    dp[now] = m + 1;
  }
}
int main() {
  input();
  findPrime();
  solve();
  printf("%d\n", res);
  return 0;
}

```