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 Counter, deque
from random import randint

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

CA = Counter(A)
CB = Counter(B)
keys = set(A + B)
M = 0
for k in keys:
    M = max(M, CA[k] + CB[k])

if M > N:
    print('No')
    exit()

CB = CB.most_common()
L, R = [], []
for i, x in enumerate(CB):
    if i % 2 == 0:
        L.append(list(x))
    else:
        R.append(list(x))
X = deque(L + R[::-1])

y = L + R
ans = [None] * N
for i in range(N):
    if (X[0][0] != A[i]) and (X[-1][0] != A[i]):
        if X[0][1] > X[-1][1]:
            ans[i] = X[0][0]
            X[0][1] -= 1
            if X[0][1] == 0:
                X.popleft()
        else:
            ans[i] = X[-1][0]
            X[-1][1] -= 1
            if X[-1][1] == 0:
                X.pop()

    elif X[0][0] != A[i]:
        ans[i] = X[0][0]
        X[0][1] -= 1
        if X[0][1] == 0:
            X.popleft()
    else:
        ans[i] = X[-1][0]
        X[-1][1] -= 1
        if X[-1][1] == 0:
            X.pop()


for i in range(10):
    m = randint(0, N - 1)
    for i in range(N):
        if ans[i] != A[i]:
            continue
        ans[i], ans[m] = ans[m], ans[i]
        m += 1
        m %= N
print('Yes')
print(*ans, sep=' ')