#include <bits/stdc++.h>
int dp[100100];
const int N = 100100;
int pr[N], p[N / 10], lp, factor[20];
int max(int x, int y) { return x > y ? x : y; }
void gp() {
  for (int i = 2; i < N; i++) {
    if (!pr[i]) p[lp++] = pr[i] = i;
    for (int j = 0; j < lp && i * p[j] < N; j++) {
      pr[i * p[j]] = p[j];
      if (i % p[j] == 0) break;
    }
  }
}
int main() {
  int n, tem, i, j;
  gp();
  while (scanf("%d", &n) != EOF) {
    memset(dp, 0, sizeof(dp));
    for (i = 0; i < n; i++) {
      scanf("%d", &tem);
      if (tem == 1) {
        dp[1] = 1;
        continue;
      }
      int num = 0, maxlen = 0;
      while (tem != 1) {
        int tt = pr[tem];
        factor[num++] = tt;
        maxlen = max(maxlen, dp[tt]);
        while (tem % tt == 0) {
          tem /= tt;
        }
      }
      for (j = 0; j < num; j++) {
        dp[factor[j]] = maxlen + 1;
      }
    }
    int ans = 0;
    for (i = 0; i <= 100000; i++) {
      ans = max(ans, dp[i]);
    }
    printf("%d\n", 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>
int dp[100100];
const int N = 100100;
int pr[N], p[N / 10], lp, factor[20];
int max(int x, int y) { return x > y ? x : y; }
void gp() {
  for (int i = 2; i < N; i++) {
    if (!pr[i]) p[lp++] = pr[i] = i;
    for (int j = 0; j < lp && i * p[j] < N; j++) {
      pr[i * p[j]] = p[j];
      if (i % p[j] == 0) break;
    }
  }
}
int main() {
  int n, tem, i, j;
  gp();
  while (scanf("%d", &n) != EOF) {
    memset(dp, 0, sizeof(dp));
    for (i = 0; i < n; i++) {
      scanf("%d", &tem);
      if (tem == 1) {
        dp[1] = 1;
        continue;
      }
      int num = 0, maxlen = 0;
      while (tem != 1) {
        int tt = pr[tem];
        factor[num++] = tt;
        maxlen = max(maxlen, dp[tt]);
        while (tem % tt == 0) {
          tem /= tt;
        }
      }
      for (j = 0; j < num; j++) {
        dp[factor[j]] = maxlen + 1;
      }
    }
    int ans = 0;
    for (i = 0; i <= 100000; i++) {
      ans = max(ans, dp[i]);
    }
    printf("%d\n", ans);
  }
  return 0;
}

```