E. Monotonic Renumerationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n integers. Let's denote monotonic renumeration of array a as an array b consisting of n integers such that all of the following conditions are met:  b_1 = 0;  for every pair of indices i and j such that 1 \le i, j \le n, if a_i = a_j, then b_i = b_j (note that if a_i \ne a_j, it is still possible that b_i = b_j);  for every index i \in [1, n - 1] either b_i = b_{i + 1} or b_i + 1 = b_{i + 1}. For example, if a = [1, 2, 1, 2, 3], then two possible monotonic renumerations of a are b = [0, 0, 0, 0, 0] and b = [0, 0, 0, 0, 1].Your task is to calculate the number of different monotonic renumerations of a. The answer may be large, so print it modulo 998244353.InputThe first line contains one integer n (2 \le n \le 2 \cdot 10^5) — the number of elements in a.The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^9).OutputPrint one integer — the number of different monotonic renumerations of a, taken modulo 998244353.ExamplesInput
5
1 2 1 2 3
Output
2
Input
2
100 1
Output
2
Input
4
1 3 3 7
Output
4

5
1 2 1 2 3

2 
['combinatorics', 'sortings', '*1700']