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_list = list(map(int, input().split()))
B_list = list(map(int, input().split()))

total_table = {}

def make_table(l):
	table = {}
	for v in l:
		if v in table:
			table[v] += 1
		else:
			table[v] = 1
		if v in total_table:
			total_table[v] += 1
		else:
			total_table[v] = 1
	return table

A_table = make_table(A_list)
B_table = make_table(B_list)

total_list = []
for v, c in total_table.items():
	total_list.append((c, v))

total_list.sort()
total_list.reverse()

A_head = []
A_tail = []
B_head = []
B_tail = []
for c, v in total_list:
	a = A_table[v] if v in A_table else 0
	b = B_table[v] if v in B_table else 0
#	print(c, a, b)
	while a > 0 and len(A_head) + len(B_head) < N:
		A_head.append(v)
		a -= 1
	
	while b > 0 and len(A_head) + len(B_head) < N:
		B_head.append(v)
		b -= 1
	
	while a > 0:
		A_tail.append(v)
		a -= 1
	
	while b > 0:
		B_tail.append(v)
		b -= 1

#print(A_head)
#print(A_tail)
#print(B_head)
#print(B_tail)

A_tail.reverse()
B_head.reverse()

A_list = A_head + A_tail
B_list = B_tail + B_head

#print(A_list)
#print(B_list)

def check():
	for a, b in zip(A_list, B_list):
		if a == b:
			return False
	else:
		return True

if check():
	AB_list = list(zip(A_list, B_list))
	AB_list.sort()
	print("Yes")
	print(*(b for a, b in AB_list))
else:
	print("No")