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=[int(_) for _ in input().split()]
b=[int(_) for _ in input().split()]

d_a={}
d_b={}

for i in range(-1,n):
    d_a[i]=0
    d_b[i]=0

for i in range(n):
    d_a[a[i]-1]+=1
    d_b[b[i]-1]+=1

diff=0
c,d=0,0
for i in range(n):
    if d_a[i]+d_b[i]>n:
        print("No")
        exit()
    c+=d_a[i]
    d+=d_b[i-1]
    diff = max(diff,c-d)
print("Yes")
# for i in range(n):
#     print(a[i],end=" ")
# print()
for i in range(n):
    print(b[(i-diff)%n],end=" ")
print()