I. Stairstime limit per test10 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputFor a permutation p of numbers 1 through n, we define a stair array a as follows: a_i is length of the longest segment of permutation which contains position i and is made of consecutive values in sorted order: [x, x+1, \ldots, y-1, y] or [y, y-1, \ldots, x+1, x] for some x \leq y. For example, for permutation p = [4, 1, 2, 3, 7, 6, 5] we have a = [1, 3, 3, 3, 3, 3, 3]. You are given the stair array a. Your task is to calculate the number of permutations which have stair array equal to a. Since the number can be big, compute it modulo 998\,244\,353. Note that this number can be equal to zero.InputThe first line of input contains integer n (1 \le n \le 10^5)  — the length of a stair array a.The second line of input contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le n).OutputPrint the number of permutations which have stair array equal to a. Since the number can be big, compute it modulo 998\,244\,353.ExamplesInput
6
3 3 3 1 1 1
Output
6
Input
7
4 4 4 4 3 3 3
Output
6
Input
1
1
Output
1
Input
8
2 2 2 2 2 2 1 1
Output
370
Input
4
3 2 3 1
Output
0

6
3 3 3 1 1 1

6 
['combinatorics', 'divide and conquer', 'dp', 'fft', 'math', '*3400']