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
from collections import Counter
input = sys.stdin.readline

def main():
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))

    judge_a = Counter(a)
    judge_b = Counter(b)
    judge = judge_a + judge_b
    
    flag = True
    for v in judge.values():
        if v > n:
            flag = False
    
    if flag:
        i, j = 0, 0

        cycle = 0
        while i < n and j < n:
            ii, jj = i, j
            if a[i] < b[j]:
                i += 1
                continue
            if a[i] > b[j]:
                j += 1
                continue
            if a[i] == b[j]:
                while i < n-1 and a[i] == a[i+1]:
                    i += 1
                while j < n-1 and b[j] == b[j+1]:
                    j += 1
            cycle = max(cycle, i-jj+1)
            i += 1
            j += 1
        
        ans = [0]*n
        for i in range(n):
            ans[(i+cycle)%n] = b[i]
        
        for i in range(n):
            if a[i] == ans[i]:
                print("No")
                sys.exit()
        print("Yes")
        print(*ans)
    else:
        print("No")

if __name__ == "__main__":
    main()