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 collections

n=int(input())
arr1=list(map(int,input().split()))
arr2=list(map(int,input().split()))
cnt1=collections.Counter(arr1)
cnt2=collections.Counter(arr2)
acum1=[0]*(n+1)
acum2=[0]*(n+1)
for i in range(1,n+1):
  acum1[i]=acum1[i-1]+cnt1[i]
  acum2[i]=acum2[i-1]+cnt2[i]
rotate=0
for i in range(1,n+1):
  rotate=max(rotate,acum1[i]-acum2[i-1])
ans=[0]*n
for i in range(n):
  ans[(i+rotate)%n]=arr2[i]
for i in range(n):
  if arr1[i]==ans[i]:
    print('No')
    break
else:
  print('Yes')
  print(*ans)