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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
import random

n = int(input())
a = [int(item) for item in input().split()]
b = [int(item) for item in input().split()]
# n = 10
# a = []
# b = []
# for _ in range(10):
#     a.append(random.randrange(1, 4))
#     b.append(random.randrange(1, 4))
# a.sort()
# b.sort()
# print(*a)
# print(*b)

b.reverse()

same_val = None
same_id = []
for i, (ai, bi) in enumerate(zip(a, b)):
    if ai == bi:
        same_val = ai
        same_id.append(i)

changeable = []
for i, (ai, bi) in enumerate(zip(a, b)):
    if b[i] != same_val and a[i] != same_val:
        changeable.append(i)

if len(same_id) > len(changeable):
    print("No")
    exit()
for s, c in zip(same_id, changeable):
    b[s], b[c] = b[c], b[s]

print("Yes")
print(*b)