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, Ai, Bi):
    Ci = [0] * (N + 1)
    Di = [0] * (N + 1)
    j = 0
    k = 0
    for i in range(1, N + 1):
        while j < N and Ai[j] <= i:
            j += 1
        Ci[i] = j
        while k < N and Bi[k] <= i:
            k += 1
        Di[i] = k
    # print(Ci)
    # print(Di)
    for i in range(1, N + 1):
        if Ci[i] - Ci[i - 1] + Di[i] - Di[i - 1] > N:
            print('No')
            return
    x = 0
    for i in range(1, N + 1):
        x = max(x, Ci[i] - Di[i - 1])
    print('Yes')
    # print(x)
    # print(' '.join([str(a) for a in Ai]))
    print(' '.join([str(Bi[(N - x + i) % N]) for i in range(N)]))


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

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