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
#import <Foundation/Foundation.h>
#import <stdio.h>
 
@interface Solution: NSObject
+ (BOOL)isFourAdjacentWithArray: (NSArray *)array;
@end
 
@implementation Solution
+ (BOOL)isFourAdjacentWithArray: (NSArray *)array {
  if ([array count] <= 2) {
        return NO;
    }
    NSInteger countFour = 0;
    NSInteger countTwo = 0;
  	NSInteger countAny = 0;
  	NSInteger i;
    for (i=0;i<array.count;i++) {
      	NSNumber *number = (NSNumber *)[array objectAtIndex: i];
        if (number.integerValue % 4 == 0) {
            countFour ++;
        } else if (number.integerValue == 2){
            countTwo = 1;
        } else {
          countAny ++;
        }
    }
  	countAny += countTwo;
    return countAny <= countFour + 1;
}  
@end
int main(int argc, char **argv) {
  int N;
  scanf("%d", &N);
  NSMutableArray *array = [NSMutableArray new];
  NSInteger i;
  for(i=0; i < N; i++) {
    int v;
    scanf("%d", &v);
    [array addObject: [NSNumber numberWithInteger: v]];
  }
  printf("%s", [Solution isFourAdjacentWithArray: array] ? "Yes" : "No");
  return 0;
}