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 collections import defaultdict, deque

n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))

ns = defaultdict(int)
for i in a:
    ns[i] += 1
for i in b:
    ns[i] += 1
if max(ns.values()) > n:
    print('No')
    exit()

j = -1
k = -1
md = 0
for i in range(2, n + 1):
    while j + 1 < n and a[j + 1] < i:
        j += 1
    while k + 1 < n and b[k + 1] < i - 1:
        k += 1
    md = max(md, j - k)

for i in range(n):
    if a[i] == b[(i - md) % n]:
        md += 1
        break

d = deque(b)
d.rotate(md)

print('Yes')
print(' '.join([str(x) for x in d]))