#D11658. 4-adjacent
4-adjacent
4-adjacent
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:
N a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print Yes; otherwise, print No.
Examples
Input
3 1 10 100
Output
Yes
Input
4 1 2 3 4
Output
No
Input
3 1 4 1
Output
Yes
Input
2 1 1
Output
No
Input
6 2 7 1 8 2 8
Output
Yes
inputFormat
Input
Input is given from Standard Input in the following format:
N a_1 a_2 ... a_N
outputFormat
Output
If Snuke can achieve his objective, print Yes; otherwise, print No.
Examples
Input
3 1 10 100
Output
Yes
Input
4 1 2 3 4
Output
No
Input
3 1 4 1
Output
Yes
Input
2 1 1
Output
No
Input
6 2 7 1 8 2 8
Output
Yes
样例
6
2 7 1 8 2 8Yes