atcoder#ARC066A. [ABC050C] Lining Up
[ABC050C] Lining Up
Score : points
Problem Statement
There are people, conveniently numbered through . They were standing in a row yesterday, but now they are unsure of the order in which they were standing. However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person. According to their reports, the difference above for person is .
Based on these reports, find the number of the possible orders in which they were standing. Since it can be extremely large, print the answer modulo . Note that the reports may be incorrect and thus there may be no consistent order. In such a case, print .
Constraints
Input
The input is given from Standard Input in the following format:
Output
Print the number of the possible orders in which they were standing, modulo .
5
2 4 4 0 2
4
There are four possible orders, as follows:
7
6 4 0 2 4 0 2
0
Any order would be inconsistent with the reports, thus the answer is .
8
7 5 1 1 7 3 5 3
16