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:
from collections import Counter, deque

N = int(input())
A = list(map(int, input().split())) + [N+1]
B = list(map(int, input().split())) + [N+1]
C = [0]
D = [0]

AB_cn = Counter(A+B)
if AB_cn.most_common()[0][1] > N:
    print("No")
else:
    print("Yes")
    for i in range(N+1):
        if len(C) != A[i]:
            C.extend([i]*(A[i]-len(C)))
        if len(D) != B[i]:
            D.extend([i]*(B[i]-len(D)))
    ans = -100000000000000000
    for i in range(N):
        curr = C[i+1] - D[i]
        ans= max(curr, ans)
    B = B[:-1]
    print(*[B[(i-ans)%N] for i in range(N)])