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 functools import reduce
from fractions import gcd
import math
import bisect
import itertools
import sys
input = sys.stdin.readline
INF = float("inf")


# 処理内容
def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))


    C = [0] * (N+1)
    D = [0] * (N+1)
    for i in range(N):
        C[A[i]] += 1
        D[B[i]] += 1
    for i in range(N+1):
        if C[i] + D[i] > N:
            print("No")
            return
    for i in range(N):
        C[i+1] += C[i]
        D[i+1] += D[i]
    
    x = 0
    for i in range(1, N+1):
        if x < C[i] - D[i-1]:
            x = C[i] - D[i-1]
    

    print("Yes")
    for i in range(N):
        if i != 0:
            print(" ", end="")
        print(B[(i+N-x)%N], end="")
    print("")


if __name__ == '__main__':
    main()