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 sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    from collections import Counter

    N = int(readline())
    a = list(map(int, readline().split()))
    b = list(map(int, readline().split()))

    cnt_a = Counter(a)
    cnt_b = Counter(b)

    acc_a = [0] * 200001
    acc_b = [0] * 200001

    for i in range(1, 200001):
        acc_a[i] = acc_a[i - 1] + cnt_a[i]
        acc_b[i] = acc_b[i - 1] + cnt_b[i]
        if cnt_a[i] + cnt_b[i] > N:
            return print("No")

    ans = 0
    for i in range(200000, 0, -1):
        score = acc_b[i] - acc_a[i - 1]
        ans = max(ans, score)

    print("Yes")

    res = b[ans:] + b[:ans]
    print(*res)

if __name__ == '__main__':
    main()