#include <bits/stdc++.h>
#pragma warning(disable : 4996)
using namespace std;
int IT_MAX = 1 << 21;
const int MOD = 1000000007;
const int INF = 1034567891;
const long long LL_INF = 1234567890123456789ll;
const double PI = 3.141592653589793238;
const double ERR = 1E-10;
map<int, int> Mx;
int in[100050];
vector<int> V[100050];
int dp[100050];
bool pchk[100050];
vector<int> plist;
int main() {
  int N, i, j, t;
  for (i = 2; i <= 100000; i++) {
    if (pchk[i]) continue;
    plist.push_back(i);
    for (j = 2 * i; j <= 100000; j += i) pchk[j] = true;
  }
  scanf("%d", &N);
  int ans = 0;
  for (i = 1; i <= N; i++) {
    scanf("%d", &t);
    for (auto it : plist) {
      if (it * it > t) break;
      if (t % it) continue;
      if (Mx.count(it)) V[i].push_back(Mx[it]);
      Mx[it] = i;
      while (t % it == 0) t /= it;
    }
    if (t != 1) {
      if (Mx.count(t)) V[i].push_back(Mx[t]);
      Mx[t] = i;
    }
    dp[i] = 1;
    for (auto it : V[i]) dp[i] = max(dp[i], dp[it] + 1);
    ans = max(ans, dp[i]);
  }
  return !printf("%d\n", ans);
}

### 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>
#pragma warning(disable : 4996)
using namespace std;
int IT_MAX = 1 << 21;
const int MOD = 1000000007;
const int INF = 1034567891;
const long long LL_INF = 1234567890123456789ll;
const double PI = 3.141592653589793238;
const double ERR = 1E-10;
map<int, int> Mx;
int in[100050];
vector<int> V[100050];
int dp[100050];
bool pchk[100050];
vector<int> plist;
int main() {
  int N, i, j, t;
  for (i = 2; i <= 100000; i++) {
    if (pchk[i]) continue;
    plist.push_back(i);
    for (j = 2 * i; j <= 100000; j += i) pchk[j] = true;
  }
  scanf("%d", &N);
  int ans = 0;
  for (i = 1; i <= N; i++) {
    scanf("%d", &t);
    for (auto it : plist) {
      if (it * it > t) break;
      if (t % it) continue;
      if (Mx.count(it)) V[i].push_back(Mx[it]);
      Mx[it] = i;
      while (t % it == 0) t /= it;
    }
    if (t != 1) {
      if (Mx.count(t)) V[i].push_back(Mx[t]);
      Mx[t] = i;
    }
    dp[i] = 1;
    for (auto it : V[i]) dp[i] = max(dp[i], dp[it] + 1);
    ans = max(ans, dp[i]);
  }
  return !printf("%d\n", ans);
}

```