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:
# 解説を参考に作成
# import sys
# sys.setrecursionlimit(10 ** 6)
# import bisect
# from collections import deque
# from decorator import stop_watch
# 
# 
# @stop_watch
def solve(N, A, B):
    buf = -1
    key = 0
    for i in range(N):
        if buf != A[i]:
            key = 0  # 前回(A[i - 1])と同じ値じゃなければリセット
        if A[i] == B[i]:
            for j in range(key, N):
                if A[i] != A[j] and B[j] != A[i]:
                    B[i], B[j] = B[j], B[i]
                    key = j
                    break
            else:
                print('No')
                return
        buf = A[i]
    print('Yes')
    print(' '.join([str(i) for i in B]))


if __name__ == '__main__':
    # S = input()
    N = int(input())
    # N, M = map(int, input().split())
    A = [int(i) for i in input().split()]
    B = [int(i) for i in input().split()]
    # ABi = [[int(i) for i in input().split()] for _ in range(N)]
    solve(N, A, B)

    # # test
    # from random import randint
    # from func import random_str
    # solve()