#include <bits/stdc++.h>
using namespace std;
long long max(long long x, long long y) { return x > y ? x : y; }
long long min(long long x, long long y) { return x < y ? x : y; }
void _(long long& a, long long b) {
  a = (a % 1000000007 + b % 1000000007) % 1000000007;
  a = (a + 1000000007) % 1000000007;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long dp[100001];
  memset(dp, -1, sizeof(dp));
  for (long long i = 2; i <= 100000; i++) {
    if (dp[i] == -1) {
      for (long long j = i; j <= 100000; j += i) dp[j] = i;
    }
  }
  long long dp1[100001];
  memset(dp1, 0, sizeof(dp1));
  long long n;
  cin >> n;
  long long a[n];
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    set<long long> s;
    while (a[i] != 1) {
      s.insert(dp[a[i]]);
      a[i] /= dp[a[i]];
    }
    long long d = 0;
    for (auto j : s) {
      d = max(d, 1 + dp1[j]);
    }
    for (auto j : s) {
      dp1[j] = max(dp1[j], d);
    }
  }
  long long ans = 1;
  for (long long i = 0; i <= 100000; i++) ans = max(ans, dp1[i]);
  cout << ans;
}

### 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;
long long max(long long x, long long y) { return x > y ? x : y; }
long long min(long long x, long long y) { return x < y ? x : y; }
void _(long long& a, long long b) {
  a = (a % 1000000007 + b % 1000000007) % 1000000007;
  a = (a + 1000000007) % 1000000007;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long dp[100001];
  memset(dp, -1, sizeof(dp));
  for (long long i = 2; i <= 100000; i++) {
    if (dp[i] == -1) {
      for (long long j = i; j <= 100000; j += i) dp[j] = i;
    }
  }
  long long dp1[100001];
  memset(dp1, 0, sizeof(dp1));
  long long n;
  cin >> n;
  long long a[n];
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    set<long long> s;
    while (a[i] != 1) {
      s.insert(dp[a[i]]);
      a[i] /= dp[a[i]];
    }
    long long d = 0;
    for (auto j : s) {
      d = max(d, 1 + dp1[j]);
    }
    for (auto j : s) {
      dp1[j] = max(dp1[j], d);
    }
  }
  long long ans = 1;
  for (long long i = 0; i <= 100000; i++) ans = max(ans, dp1[i]);
  cout << ans;
}

```