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 random
N=int(input())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]
a=[0 for i in range(N+1)]
b=[0 for i in range(N+1)]
for i in range(N):
    a[A[i]]+=1
    b[B[i]]+=1
if max([a[i]+b[i] for i in range(1,N+1)])<=N:
    print("Yes")
else:
    print("No")
    exit()
B=B[::-1]
point=0
for i in range(N):
    if A[i]==B[i]:
        point+=1
while(point>0):
    x=random.randrange(N)
    y=random.randrange(N)
    if x==y:
        continue
    before=0
    after=0
    if A[x]==B[x]:
        before+=1
    if A[y]==B[y]:
        before+=1
    if A[x]==B[y]:
        after+=1
    if A[y]==B[x]:
        after+=1
    if before>after:
        B[x],B[y]=B[y],B[x]
        point=point+after-before
print(*B)