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:
import collections
import sys

def solve(n, A, B):
  ans = B[:]
  same = collections.deque()
  for i, (a, b) in enumerate(zip(A, B)):
    if a == b:
      if same and B[same[0]] != a:
        j = same.popleft()
        B[i], B[j] = B[j], B[i]
      else:
        same.append(i)
 # print(A)
  #print(B)
  #print(same)
  if same:
    s = A[same[0]]
    to_swap = []
    possible = False
    for i, (a, b) in enumerate(zip(A, B)):
      if a != s and b!=s:
        to_swap.append(i)
      if len(to_swap) == len(same):
        possible = True
        break
    if not possible:
      print('No')
      return
    for i, j in zip(same, to_swap):
      B[i], B[j] = B[j], B[i]
  print('Yes')
  print(*B,sep=' ')


       


def main():
  input = sys.stdin.readline
  n = int(input())
  A = list(map(int, input().split()))
  B = list(map(int, input().split()))
  solve(n, A, B)

main()