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:
from collections import defaultdict
dic = defaultdict(int)
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
for x,y in zip(A,B):
  dic[x] += 1
  dic[y] += 1
L = list(dic.values())
MAX = max(L)
if MAX > N:
  print("No"); exit()
INF = float("inf")
dicA_min = defaultdict(lambda: INF); dicA_max = defaultdict(lambda: 0)
dicB_min = defaultdict(lambda: INF); dicB_max = defaultdict(lambda: 0)
for i in range(N):
  dicA_min[A[i]] = min(dicA_min[A[i]],i)
  dicA_max[A[i]] = max(dicA_max[A[i]],i)
  dicB_min[B[i]] = min(dicB_min[B[i]],i)
  dicB_max[B[i]] = max(dicB_max[B[i]],i)
#print(dicA_min,dicA_max)
L = list(dicB_min.keys())
mink = -INF
maxk = INF
Flag = False
for t in L:
  if dicA_min[t] == INF:
    continue
  mink = max(dicA_max[t]-dicB_min[t]+1,mink)
  maxk = min(dicA_min[t]+N-dicB_max[t]-1,maxk)
  Flag = True
if not Flag:
  print("Yes")
  print(*B)
  exit()
#print(mink,maxk)
if mink >= 0:
  ans = B[-mink:] + B[:-mink]
else:
  ans = B[-mink:] + B[:-mink]
print("Yes")
print(*ans)