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:
def numcount(x):
    ans=[0]*n
    res=1
    for i in range(n-1):
        if x[i]!=x[i+1]:
            ans[x[i]-1]=res
            res=0
        res+=1
    ans[x[n-1]-1]=res
    return ans

n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))

a2=numcount(a)
b2=numcount(b)
ans1=False
for i in range(n):
    if a2[i]+b2[i]>n:
        ans1=True
        break


ans2=a2[0]
res=a2[0]
for i in range(n-1):
    res+=a2[i+1]-b2[i]
    ans2=max(ans2,res)


if ans1:
    print("No")
else:
    print("Yes")
    c=[0]*n
    for i in range(n):
        c[(i+ans2)%n]=b[i]
    print(" ".join([str(n) for n in c]))