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()))

AB = [(a, i, 0) for i, a in enumerate(A)] + [(b, i, 1) for i, b in enumerate(B)]
AB.sort()

X = AB[:N]
Y = AB[N:]

if any(x[0] == y[0] for x, y in zip(X, Y)):
    print('No')
    exit()

swapA = []
swapB = []
ans = [-1] * N

for (_, i, sx), (_, j, sy) in zip(X, Y):
    if sx == sy == 0:
        swapA.append((i, j))
    elif sx == sy == 1:
        swapB.append((i, j))
    else:
        if sx == 0:
            ans[i] = B[j]
        else:
            ans[j] = B[i]

for (i, j), (x, y) in zip(swapA, swapB):
    ans[i] = B[x]
    ans[j] = B[y]

    if A[i] == ans[i] or A[j] == ans[j]:
        ans[i], ans[j] = ans[j], ans[i]

print('Yes')
print(*ans)