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:
from itertools import groupby

n = int(input())
aaa = list(map(int, input().split()))
bbb = list(map(int, input().split()))

idx_a = {}
cnt_a = {}
i = 0
for a, itr in groupby(aaa):
    cnt = len(list(itr))
    i += cnt
    idx_a[a] = i
    cnt_a[a] = cnt

idx_b = {}
cnt_b = {}
i = 0
for b, itr in groupby(bbb):
    cnt = len(list(itr))
    idx_b[b] = i
    cnt_b[b] = cnt
    i += cnt

slide = 0
for a in idx_a:
    if a not in idx_b:
        continue
    if cnt_a[a] + cnt_b[a] > n:
        print('No')
        exit()
    slide = max(slide, idx_a[a] - idx_b[a])

print('Yes')
if slide > 0:
    bbb = bbb[-slide:] + bbb[:-slide]
print(*bbb)