#include <bits/stdc++.h>
using namespace std;
const long long MOD9 = 1e9 + 7;
const long long MAX = 1e5 + 10;
const double eps = 0.99;
int dx[4] = {0, 0, 1, -1};
int dy[4] = {-1, 1, 0, 0};
int t, n, m = 0, q, k;
bool a[MAX];
int dp[MAX];
int f(long long i) {
  if (i <= 0) return 0;
  int& ret = dp[i];
  if (ret != -1) return ret;
  ret = a[i];
  for (long long j = 2; j * j <= i; j++) {
    if (i % j == 0) {
      ret = max(ret, a[i] + f(j));
      ret = max(ret, a[i] + f(i / j));
    }
  }
  m = max(m, ret);
  for (long long j = 2; j * j <= i; j++) {
    if (i % j == 0) {
      dp[j] = max(ret, dp[j]);
      dp[i / j] = max(ret, dp[i / j]);
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  memset(dp, -1, sizeof(dp));
  int x = 0;
  for (long long i = 0; i < n; i++) cin >> t, a[t]++, x = max(x, t);
  dp[1] = a[1];
  int mx = 0;
  for (long long i = 0; i < x + 1; i++) {
    if (a[i]) mx = max(mx, f(i));
  }
  cout << mx;
}

### 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;
const long long MOD9 = 1e9 + 7;
const long long MAX = 1e5 + 10;
const double eps = 0.99;
int dx[4] = {0, 0, 1, -1};
int dy[4] = {-1, 1, 0, 0};
int t, n, m = 0, q, k;
bool a[MAX];
int dp[MAX];
int f(long long i) {
  if (i <= 0) return 0;
  int& ret = dp[i];
  if (ret != -1) return ret;
  ret = a[i];
  for (long long j = 2; j * j <= i; j++) {
    if (i % j == 0) {
      ret = max(ret, a[i] + f(j));
      ret = max(ret, a[i] + f(i / j));
    }
  }
  m = max(m, ret);
  for (long long j = 2; j * j <= i; j++) {
    if (i % j == 0) {
      dp[j] = max(ret, dp[j]);
      dp[i / j] = max(ret, dp[i / j]);
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  memset(dp, -1, sizeof(dp));
  int x = 0;
  for (long long i = 0; i < n; i++) cin >> t, a[t]++, x = max(x, t);
  dp[1] = a[1];
  int mx = 0;
  for (long long i = 0; i < x + 1; i++) {
    if (a[i]) mx = max(mx, f(i));
  }
  cout << mx;
}

```