#include <bits/stdc++.h>
using namespace std;
int fac[100000];
int dp[100001];
int mulbest[100001];
int main() {
  for (int i = 0; i <= 100000; i++) fac[i] = i;
  for (int i = 2; i <= 320; i++) {
    if (fac[i] != i) continue;
    fac[i] = i;
    for (int j = 2 * i; j <= 100000; j += i) fac[j] = i;
  }
  int N;
  scanf("%d", &N);
  int bestest = 0;
  for (int i = 0; i < N; i++) {
    int a;
    scanf("%d", &a);
    int best = 1;
    int cur = a;
    while (cur != 1) {
      best = max(best, mulbest[fac[cur]] + 1);
      cur /= fac[cur];
    }
    cur = a;
    while (cur != 1) {
      mulbest[fac[cur]] = max(mulbest[fac[cur]], best);
      cur /= fac[cur];
    }
    dp[i] = best;
    bestest = max(bestest, best);
  }
  printf("%d\n", bestest);
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 fac[100000];
int dp[100001];
int mulbest[100001];
int main() {
  for (int i = 0; i <= 100000; i++) fac[i] = i;
  for (int i = 2; i <= 320; i++) {
    if (fac[i] != i) continue;
    fac[i] = i;
    for (int j = 2 * i; j <= 100000; j += i) fac[j] = i;
  }
  int N;
  scanf("%d", &N);
  int bestest = 0;
  for (int i = 0; i < N; i++) {
    int a;
    scanf("%d", &a);
    int best = 1;
    int cur = a;
    while (cur != 1) {
      best = max(best, mulbest[fac[cur]] + 1);
      cur /= fac[cur];
    }
    cur = a;
    while (cur != 1) {
      mulbest[fac[cur]] = max(mulbest[fac[cur]], best);
      cur /= fac[cur];
    }
    dp[i] = best;
    bestest = max(bestest, best);
  }
  printf("%d\n", bestest);
  return 0;
}

```