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 deque

n=int(input())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]
ans=[-1 for i in range(n)]

newB=[]
cnt=1
old=B[0]
for i in range(1,n):
    if old!=B[i]:
        newB.append((old,cnt))
        cnt=1
        old=B[i]
    else:
        cnt+=1
else:
    newB.append((old,cnt))
B=deque(newB)

def firstDec():
    now=B.popleft()
    if now[1]>1:
        B.appendleft((now[0],now[1]-1))

tori=0

for i in range(n):
    if B[0][0]!=A[i]:
        ans[i]=B[0][0]
        firstDec()
        continue

    B.rotate(-1)
    if B[0][0]!=A[i]:
        ans[i]=B[0][0]
        firstDec()
        continue
    
    OK=False
    while tori<i:
        if ans[tori]!=B[0][0] and A[tori]!=B[0][0]:
            ans[i]=ans[tori]
            ans[tori]=B[0][0]
            OK=True
            break
        B.rotate()
        if ans[tori]!=B[0][0] and A[tori]!=B[0][0]:
            ans[i]=ans[tori]
            ans[tori]=B[0][0]
            OK=True
            break
        tori+=1
    if OK:
        continue
    
    print("No")
    break
else:
    print("Yes")
    print(" ".join([str(num) for num in ans]))