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You are given an integer $$$n$$$ and a sequence of integers $$$a_1, a_2, \ldots, a_n$$$. Your task is to determine the number of integer sequences $$$(b_1, b_2, \ldots, b_n)$$$ such that the following conditions are satisfied:

$$$1 \leq b_i \leq a_i$$$ for each $$$i$$$ ($$$1 \le i \le n$$$).
$$$b_i$$$ is a factor of $$$b_{i+1}$$$ for each $$$i$$$ ($$$1 \le i \le n-1$$$).

Two sequences are considered different if they differ in at least one position.

Since the number of such sequences may be large, compute the answer modulo $$$998\,244\,353$$$.

Input

The first line of input contains a single integer $$$n$$$ ($$$1 \le n \le 200\,000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 200\,000$$$).

Output

Output the number of distinct sequences satisfying the conditions, modulo $$$998\,244\,353$$$.

Growth Factor

Examples