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(map(int, input().split()))
b = list(map(int, input().split()))
be = [-1] * n
la = [-1] * n
be2 = [-1] * n
la2 = [-1] * n
for i in range(n):
    if be[a[i] - 1] == -1:
        be[a[i] - 1] = i
    la[a[i] - 1] = i + 1
    if be2[b[i] - 1] == -1:
        be2[b[i] - 1] = i
    la2[b[i] - 1] = i + 1
l, r = 0, 2 * n
for i in range(n):
    if la[i] != -1 and la2[i] != -1:
        l = max(la[i] - be2[i], l)
        r = min(r, be[i] + n - la2[i])
if l > r:
    print('No')
else:
    print('Yes')
    print(*(b[n-l:] + b[:n-l]))