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
readline = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7
#mod = 998244353
INF = 10**18
eps = 10**-7

n = int(readline())
a = list(map(int,readline().split()))
b = list(map(int,readline().split()))

c = [0]*(n+1)
d = [0]*(n+1)

for ai in a:
    c[ai] += 1

for bi in b:
    d[bi] += 1

for i in range(n+1):
    if (c[i]+d[i] > n):
        print("No")
        exit()
print("Yes")

for i in range(n):
    c[i+1] += c[i]
    d[i+1] += d[i]

divi = 0

for i in range(1,n+1):
    divi = max(divi, c[i]-d[i-1])

divi = n-divi

ans = b[divi:] + b[:divi]

print(" ".join(map(str, ans)))