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())
A=list(map(int, input().split()))
B=list(map(int, input().split()))

C=[0]*(N+1)
D=[0]*(N+1)
E=[0]*(N+1)

for i in range(N):
  C[A[i]]+=1
  D[B[i]]+=1
  E[A[i]]+=1
  E[B[i]]+=1

if max(E)>N:
  print("No")
  exit()
  
for i in range(1,N+1):
  C[i]+=C[i-1]
  D[i]+=D[i-1]

ans=0
for i in range(1,N+1):
  ans=max(ans, C[i]-D[i-1])
B=[B[(i-ans)%N] for i in range(N)]
  
print("Yes")
print(' '.join(map(str, B)))