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:
import sys,queue,math,copy,itertools,bisect,collections,heapq

def main():
    LI = lambda : [int(x) for x in sys.stdin.readline().split()]
    NI = lambda : int(sys.stdin.readline())

    N = NI()
    A = LI()
    B = LI()

    c = collections.Counter()
    for x in A:
        c[x] += 1
    for x in B:
        c[x] += 1
        if c[x] > N:
            print('No')
            return

    s = 0
    for i in range(N):
        if A[i] == B[i]:

            p = bisect.bisect_left(B,B[i]+1,i+1)
            if p > N-1:
                p = s
                s += 1
                while B[i] == B[s]:
                    s+=1

            B[i],B[p] = B[p],B[i]
    print('Yes')
    print(*B,sep=' ')

if __name__ == '__main__':
    main()