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:
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

start = 0
ind = 0
NG = [0]*(2*N+1)

bdic = {}
for i, b in enumerate(B):
    if not b in bdic:
        bdic[b] = [i, i]
    else:
        bdic[b] = [min(bdic[b][0], i), max(bdic[b][1], i)]


for i, a in enumerate(A):
    if a in bdic:
        j1, j2 = bdic[a]
        if j1 >= i:
            NG[j1-i] += 1
            NG[j2-i+1] -= 1
        elif j2 < i:
            NG[j1-i+N] += 1
            NG[j2-i+1+N] -= 1
        else:
            NG[j1-i+N] += 1
            NG[0] += 1
            NG[j2-i+1] -= 1

start = -1
for i in range(N):
    if NG[i] == 0:
        start = i
        break
    NG[i+1] += NG[i]

if start == -1:
    print("No")
else:
    print("Yes")
    ans = []
    for i in range(N):
        ans.append(B[(i+start)%N])
    print(*ans)