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()))
from collections import Counter,deque
x,y=Counter(a),Counter(b)
for i in range(1,n+1):
    if x[i]+y[i]>n:
        print("No")
        exit()
ans=b[::-1]
change=deque()
num=-1
now=deque()
for i in range(n):
    if a[i]==ans[i]:
        change.append(i)
        num=ans[i]
    else:
        now.append(i)
if change==[]:
    print("Yes")
    print(" ".join(map(str,ans)))
    exit()
while len(change):
    q=now.popleft()
    p=change.popleft()
    if a[q]!=num and ans[q]!=num:
        ans[q],ans[p]=ans[p],ans[q]
    else:
        change.appendleft(p)

print("Yes")
print(" ".join(map(str,ans)))