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:
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
judge = True

A_num = [0] * (N+1)
B_num = [0] * (N+1)
C = [0] * (N+1)
D = [0] * (N+1)

for a in A:
  A_num[a] += 1
for b in B:
  B_num[b] += 1
  
for a,b in zip(A_num,B_num):
  if a+b>N:
    judge = False
    break

if judge:
  for i in range(1,N+1):
    C[i] = C[i-1] + A_num[i]
    D[i] = D[i-1] + B_num[i]
  x = -float('inf')
  for i in range(1,N+1):
    x = max(x, C[i] - D[i-1])
    
  ans = B[-x:] + B[:-x]
  print('Yes')
  print(' '.join(map(str,ans)))
  
else:
  print('No')