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:
mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

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

    B.reverse()
    idx = []
    x = -1
    for i in range(N):
        if A[i] == B[i]:
            idx.append(i)
            x = A[i]
    if len(idx) == 0:
        print("Yes")
        print(*B)
    else:
        l = 0
        r = N-1
        for i in idx:
            if A[l] != x and B[l] != x:
                B[l], B[i] = B[i], B[l]
                l += 1
            else:
                if A[r] != x and B[r] != x:
                    B[r], B[i] = B[i], B[r]
                    r -= 1
                else:
                    print("No")
                    exit()
        print("Yes")
        print(*B)


if __name__ == '__main__':
    main()