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:
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
cnta = [0]*(n+1)
cntb = [0]*(n+1)
ta = 0
tb = 0
s = [0]*(n+1)
for i in range(n):
    cnta[a[i]] += 1
    cntb[b[i]] += 1
    s[a[i]] += 1
    s[b[i]] += 1
if max(s) > n:
    print("No")
    exit()
print("Yes")
m = 0
for i in range(1,n+1):
    cnta[i] += cnta[i-1]
    cntb[i] += cntb[i-1]
for i in range(1,n+1):
    m = max(m,cnta[i]-cntb[i-1])
# print(m)
# print(cnta)
# print(cntb)
print(*b[-m:]+b[0:-m])