You are exploring the stunning region of Natlan! This region consists of (n) cities, and each city is rated with an attractiveness (a_i). A directed edge exists from City (i) to City (j) if and only if (i < j) and (\gcd(a_i,a_j)\neq 1), where (\gcd(x, y)) denotes the greatest common divisor (GCD) of integers (x) and (y). Starting from City (1), your task is to determine the total number of distinct paths you can take to reach City (n), modulo (998\,244\,353). Two paths are different if and only if the set of cities visited is different. The first line contains an integer (n) ((2 \leq n \leq 2 \cdot 10^5)) — the number of cities. The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((2 \leq a_i \leq 10^6)) — the attractiveness of each city. Output the total number of distinct paths you can take to reach City (n), modulo (998\,244\,353). In the first example, the five paths are the following: City (1\rightarrow) City (5) City (1\rightarrow) City (2\rightarrow) City (5) City (1\rightarrow) City (2\rightarrow) City (3\rightarrow) City (5) City (1\rightarrow) City (2\rightarrow) City (4\rightarrow) City (5) City (1\rightarrow) City (4\rightarrow) City (5) In the second example, the two paths are the following: City (1\rightarrow) City (3\rightarrow) City (5) City (1\rightarrow) City (2\rightarrow) City (3\rightarrow) City (5)