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
input = sys.stdin.readline
n = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))

from random import randint
# n = 3
# l = n
# A = [randint(1,l) for i in range(n)]
# B = [randint(1,l) for i in range(n)]
# A.sort()
# B.sort()
# print(A,B)

# A = [1,1,2,4,5]
# B = [1,1,2,3,5]

C = [-1] * (n+2)
D = [-1] * (n+2)
for i in range(1, n):
    if A[i-1] != A[i]:
        C[A[i-1]] = i-1
C[A[-1]] = n-1

ind = 0
D[B[0]] = 0
for i in range(1, n):
    if B[i-1] != B[i]:
        D[B[i]] = i

# print(C,D)

sh = 0
for i in range(n+2):
    if C[i] != -1 and D[i] != -1:
        sh = max(sh, C[i]-D[i]+1)

# print("sh",sh)

N = [B[(i-sh)%n] for i in range(n)]
ng = 0
# print("N",N)
for i in range(n):
    if N[i] == A[i]:
        ng = 1
        break

if ng == 1:
    print("No")
else:
    print("Yes")
    print(*N)