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:
#解説参照
n=int(input())
*a,=map(int, input().split())
*b,=map(int, input().split())
shift=0
from bisect import bisect_right,bisect_left
from collections import Counter
sb=Counter(b)
sa=Counter(a)
for bi in sb:
    if bi in sa:
        if sa[bi]+sb[bi]>n:
            print("No")
            exit()
for bi in sb:
    lb=bisect_left(b,bi)
    ra=bisect_right(a,bi)
    if a[ra-1]==b[lb]:
        shift=max(shift,ra-lb)
ans=[b[(i-shift)%n] for i in range(n)]##
print("Yes")
print(*ans)