#include <bits/stdc++.h>
using namespace std;
const int INF = (-1u) / 2;
const long long int INF2 = (-1ull) / 2;
int a, b, i, d[1011000], j, k, n, m, timer = 0, l, r, x, y;
int c[1011000], cnt = 0, fl = 0, a2, a3 = -1000000, ans = 0;
vector<int> v;
void deb(bool a) {
  if (a) return;
  printf("PROGRAM TERMINATED\n");
  exit(0);
}
int main() {
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &c[i]);
    k = sqrt(c[i]);
    if (v.size()) v.clear();
    ans = 0;
    for (j = 1; j <= k; j++) {
      if (c[i] % j == 0) {
        v.push_back(j);
        if (j * j != c[i]) {
          v.push_back(c[i] / j);
        }
        if (j != 1) ans = max(ans, d[j]);
        ans = max(ans, d[c[i] / j]);
      }
    }
    for (j = 1; j < v.size(); j++) {
      d[v[j]] = max(d[v[j]], ans + 1);
    }
  }
  ans = 0;
  for (i = 2; i <= 100000; i++) {
    ans = max(ans, d[i]);
  }
  ans = max(ans, 1);
  printf("%d\n", ans);
  return 0;
}

### Prompt

Your challenge is to write 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;
const int INF = (-1u) / 2;
const long long int INF2 = (-1ull) / 2;
int a, b, i, d[1011000], j, k, n, m, timer = 0, l, r, x, y;
int c[1011000], cnt = 0, fl = 0, a2, a3 = -1000000, ans = 0;
vector<int> v;
void deb(bool a) {
  if (a) return;
  printf("PROGRAM TERMINATED\n");
  exit(0);
}
int main() {
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &c[i]);
    k = sqrt(c[i]);
    if (v.size()) v.clear();
    ans = 0;
    for (j = 1; j <= k; j++) {
      if (c[i] % j == 0) {
        v.push_back(j);
        if (j * j != c[i]) {
          v.push_back(c[i] / j);
        }
        if (j != 1) ans = max(ans, d[j]);
        ans = max(ans, d[c[i] / j]);
      }
    }
    for (j = 1; j < v.size(); j++) {
      d[v[j]] = max(d[v[j]], ans + 1);
    }
  }
  ans = 0;
  for (i = 2; i <= 100000; i++) {
    ans = max(ans, d[i]);
  }
  ans = max(ans, 1);
  printf("%d\n", ans);
  return 0;
}

```