#AT1111. C - 4-adjacent
C - 4-adjacent
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C - 4-adjacent
Score : $400$ points
Problem Statement
We have a sequence of length $N$, $a = (a_1, a_2, ..., a_N)$. Each $a_i$ is a positive integer.
Snuke's objective is to permute the element in $a$ so that the following condition is satisfied:
- For each $1 ≤ i ≤ N - 1$, the product of $a_i$ and $a_{i + 1}$ is a multiple of $4$.
Determine whether Snuke can achieve his objective.
Constraints
- $2 ≤ N ≤ 10^5$
- $a_i$ is an integer.
- $1 ≤ a_i ≤ 10^9$
Input
Input is given from Standard Input in the following format:
Output
If Snuke can achieve his objective, print Yes
; otherwise, print No
.
3
1 10 100
Yes
One solution is $(1, 100, 10)$.
4
1 2 3 4
No
It is impossible to permute $a$ so that the condition is satisfied.
3
1 4 1
Yes
The condition is already satisfied initially.
2
1 1
No
6
2 7 1 8 2 8
Yes