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 = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]
C = [0]*N
D = [0]*N
c = d = 0
for i in range(N):
    a = A[i]
    b = B[i]
    if C[a-1]==0:
        for j in range(c,a): C[j]=C[c]
        c=a-1
        C[c]=C[c-1]+1
    else: C[a-1]+=1
    if D[b-1]==0:
        for j in range(d,b): D[j]=D[d]
        d=b-1
        D[d]=D[d-1]+1
    else: D[b-1]+=1
for j in range(c,N): C[j]=C[c]
for j in range(d,N): D[j]=D[d]
E = [0]*N
for i in range(N):
    if i==0: E[i] = C[i] + D[i]
    else:
        E[i] = C[i]-C[i-1] + D[i]-D[i-1]
#print(C,D,E)
if max(E)>N: print("No")
else:
    for i in range(N):
        if i==0: x=C[i]
        if x < C[i]-D[i-1]: x = C[i]-D[i-1]
    B_ = [0]*N
    #print(x)
    for i in range(N):
        B_[(i+x)%N] = B[i]
    print("Yes")
    print(*B_,sep=' ')