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A. Array Without Local Maximums
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Ivan unexpectedly saw a present from one of his previous birthdays. It is array of n numbers from 1 to 200. Array is old and some numbers are hard to read. Ivan remembers that for all elements at least one of its neighbours ls not less than it, more formally:

a1a2,

anan1 and

aimax(ai1,ai+1) for all i from 2 to n1.

Ivan does not remember the array and asks to find the number of ways to restore it. Restored elements also should be integers from 1 to 200. Since the number of ways can be big, print it modulo 998244353.

Input

First line of input contains one integer n (2n105) — size of the array.

Second line of input contains n integers ai — elements of array. Either ai=1 or 1ai200. ai=1 means that i-th element can't be read.

Output

Print number of ways to restore the array modulo 998244353.

Examples
Input
3
1 -1 2
Output
1
Input
2
-1 -1
Output
200
Note

In the first example, only possible value of a2 is 2.

In the second example, a1=a2 so there are 200 different values because all restored elements should be integers between 1 and 200.