#include <bits/stdc++.h>
using namespace std;
const int MAXN = 100009;
int p[MAXN], pn;
bool notp[MAXN];
vector<int> fac[MAXN];
void pre() {
  int i, j;
  for (i = 2; i < MAXN; ++i) {
    if (!notp[i]) {
      p[pn++] = i;
      for (j = i; j < MAXN; j += i) fac[j].push_back(i);
    }
    for (j = 0; j < pn && i * p[j] < MAXN; ++j) {
      notp[i * p[j]] = true;
      if (i % p[j] == 0) break;
    }
  }
}
int a[MAXN], dp[MAXN];
void checkMax(int &a, int t) {
  if (t > a) a = t;
}
int main() {
  pre();
  int i, j, n, t, ans;
  while (scanf("%d", &n) != EOF) {
    for (i = 0; i < n; ++i) scanf("%d", a + i);
    fill(dp, dp + MAXN, 0);
    for (i = 0; i < n; ++i) {
      t = 0;
      for (j = 0; j < fac[a[i]].size(); ++j) {
        t = max(t, dp[fac[a[i]][j]]);
      }
      for (j = 0; j < fac[a[i]].size(); ++j) checkMax(dp[fac[a[i]][j]], t + 1);
    }
    ans = *max_element(dp, dp + MAXN);
    printf("%d\n", max(1, ans));
  }
  return 0;
}

### 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 int MAXN = 100009;
int p[MAXN], pn;
bool notp[MAXN];
vector<int> fac[MAXN];
void pre() {
  int i, j;
  for (i = 2; i < MAXN; ++i) {
    if (!notp[i]) {
      p[pn++] = i;
      for (j = i; j < MAXN; j += i) fac[j].push_back(i);
    }
    for (j = 0; j < pn && i * p[j] < MAXN; ++j) {
      notp[i * p[j]] = true;
      if (i % p[j] == 0) break;
    }
  }
}
int a[MAXN], dp[MAXN];
void checkMax(int &a, int t) {
  if (t > a) a = t;
}
int main() {
  pre();
  int i, j, n, t, ans;
  while (scanf("%d", &n) != EOF) {
    for (i = 0; i < n; ++i) scanf("%d", a + i);
    fill(dp, dp + MAXN, 0);
    for (i = 0; i < n; ++i) {
      t = 0;
      for (j = 0; j < fac[a[i]].size(); ++j) {
        t = max(t, dp[fac[a[i]][j]]);
      }
      for (j = 0; j < fac[a[i]].size(); ++j) checkMax(dp[fac[a[i]][j]], t + 1);
    }
    ans = *max_element(dp, dp + MAXN);
    printf("%d\n", max(1, ans));
  }
  return 0;
}

```