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 collections
import heapq

N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

def construct():
    A_queue = [(-c, x) for x, c in collections.Counter(A).items()]
    heapq.heapify(A_queue)
    index = [None]*(N+1)
    for i, a in enumerate(A):
        if index[a] is None:
            index[a] = i

    B_queue = [(-c, x) for x, c in collections.Counter(B).items()]
    heapq.heapify(B_queue)

    answer = [None]*N

    while B_queue:
        neg_cb, b = heapq.heappop(B_queue)

        neg_ca, a = heapq.heappop(A_queue)
        if a == abs(b):
            if not A_queue: return None
            hold = (neg_ca, a)
            neg_ca, a = heapq.heappop(A_queue)
        else:
            hold = None

        answer[index[a]] = b
        index[a] += 1
        if neg_cb < -1:
            heapq.heappush(B_queue, (neg_cb+1, b))
        if neg_ca < -1:
            heapq.heappush(A_queue, (neg_ca+1, a))
        if hold is not None:
            heapq.heappush(A_queue, hold)
    else:
        return answer

answer = construct()
if answer is None:
    B = [-x for x in B]
    answer = construct()
    if answer is not None:
        answer = [-x for x in answer]

if answer:
    print('Yes')
    print(*answer)
else:
    print('No')