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 python


def main():
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    b = list(reversed(b))
    bad = next((x for x, y in zip(a, b) if x == y), None)
    if bad is None:
        print('Yes')
        print(' '.join(map(str, b)))
    else:
        l_1 = sum(1 for x, y in zip(a, b) if x < bad < y)
        l_2 = sum(1 for x, y in zip(a, b) if x < y and bad in (x, y))
        l_3 = sum(1 for x, y in zip(a, b) if x == y)
        l_4 = sum(1 for x, y in zip(a, b) if x > y and bad in (x, y))
        l_5 = sum(1 for x, y in zip(a, b) if x > bad > y and x != bad)
        if l_3 > l_1 + l_5:
            print('No')
        else:
            good_part = b[:l_1] + b[l_1 + l_2 + l_3 + l_4:]
            bad_part = b[l_1 + l_2:l_1 + l_2 + l_3]
            b[l_1 + l_2:l_1 + l_2 + l_3] = good_part[:l_3]
            good_part[:l_3] = bad_part
            b[:l_1] = good_part[:l_1]
            b[l_1 + l_2 + l_3 + l_4:] = good_part[l_1:]
            assert all(x != y for x, y in zip(a, b))
            print('Yes')
            print(' '.join(map(str, b)))


if __name__ == '__main__':
    main()