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:
# coding: utf-8
# Your code here!
import sys
readline = sys.stdin.readline
read = sys.stdin.read

n, = map(int,readline().split())
*a, = map(int,readline().split())
*b, = map(int,readline().split())
b = b[::-1]

same = [i for i in range(n) if a[i] == b[i]]
if same:
    v = a[same[0]] # b を逆順にしたので、重なる値は一種類しかない。これを v とおく。
    r = same[0]
    s = same[-1]+1
    notv = [i for i in range(n) if a[i]!=v and b[i]!=v] # どっちもvとかぶらない index
    if len(same) > len(notv):
        print("No")
        exit()
    
    for i,j in zip(same,notv):
        b[i],b[j] = b[j],b[i]

print("Yes")
print(*b)