Problem: Given are two sequences A and B, both of length N. A and B are each sorted in the ascending order. Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

* 1\leq N \leq 2 \times 10^5
* 1\leq A_i,B_i \leq N
* A and B are each sorted in the ascending order.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


Output

If there exist no reorderings that satisfy the condition, print `No`.

If there exists a reordering that satisfies the condition, print `Yes` on the first line. After that, print a reordering of B on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

Examples

Input

6
1 1 1 2 2 3
1 1 1 2 2 3


Output

Yes
2 2 3 1 1 1


Input

3
1 1 2
1 1 3


Output

No


Input

4
1 1 2 3
1 2 3 3


Output

Yes
3 3 1 2

Solution (in PYTHON3):

Solution:
n = int(input())
lst_a = [int(i) for i in input().split()]
lst_b = [int(i) for i in input().split()]
j = 0
flag = True
for i in range(n):
  if i > 0:
    if lst_a[i] != lst_a[i - 1]:
      j = 0
  if lst_a[i] != lst_b[i]:
    continue
  else:
    flag = False
    while j != n:
      if lst_a[i] != lst_b[j] and lst_a[j] != lst_b[i]:
        lst_b[i], lst_b[j] = lst_b[j], lst_b[i]
        flag = True
        break
      j += 1
    if not flag:
      break
if not flag:
  print('No')
else:
  print('Yes')
  lst_b = [str(i) for i in lst_b]
  print(' '.join(lst_b))