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:
#!/usr/bin/env python3
from collections import Counter
INF = 1e12


def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    lA = Counter(A)
    lB = Counter(B)
    if max(Counter(A+B).values()) > N:
        print('No')
        exit()

    C = [0] * (N + 1)
    D = [0] * (N + 1)
    for i in range(N):
        C[i + 1] = lA[i + 1] + C[i]
        D[i + 1] = lB[i + 1] + D[i]
    shift = - INF
    for i in range(1, N + 1):
        shift = max(shift, C[i] - D[i - 1])
    print('Yes')
    ans = (B + B + B)[N-shift:2*N-shift]
    print(' '.join([str(a) for a in ans]))


if __name__ == "__main__":
    main()