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B. Good Sequences

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSquirrel Liss is interested in sequences. She also has preferences of integers. She thinks *n* integers *a* _{1}, *a* _{2}, ..., *a* _{ n} are good.

Now she is interested in good sequences. A sequence *x* _{1}, *x* _{2}, ..., *x* _{ k} is called good if it satisfies the following three conditions:

- The sequence is strictly increasing, i.e.
*x*_{ i}<*x*_{ i + 1}for each*i*(1 ≤*i*≤*k*- 1). - No two adjacent elements are coprime, i.e.
*gcd*(*x*_{ i},*x*_{ i + 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* ≤ 10^{5}) — the number of good integers. The second line contains a single-space separated list of good integers *a* _{1}, *a* _{2}, ..., *a* _{ n} in strictly increasing order (1 ≤ *a* _{ i} ≤ 10^{5}; *a* _{ i} < *a* _{ i + 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.

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