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()))

cnt = [[0,i] for i in range(n+1)]
cnt_a = [0] * (n+1)
cnt_b = [0] * (n+1)

for ai,bi in zip(a,b):
    cnt[ai][0] += 1
    cnt[bi][0] += 1
    cnt_a[ai] += 1
    cnt_b[bi] += 1

cnt.sort(reverse=True)
new_al = []
new_ar = []
new_bl = []
new_br = []
done = 0
for _,i in cnt:
    if(done >= n):
        new_ar += [i] * cnt_a[i]
        new_bl += [i] * cnt_b[i]
    elif(done + cnt_a[i] + cnt_b[i] <= n):
        new_al += [i] * cnt_a[i]
        new_br += [i] * cnt_b[i]
    else:
        if(cnt_a[i] > n-done):
            new_al += [i] * (n-done)
            new_ar += [i] * (cnt_a[i] - n + done)
            new_bl += [i] * cnt_b[i]
        else:
            new_al += [i] * cnt_a[i]
            new_br += [i] * (n - done - cnt_a[i])
            new_bl += [i] * (cnt_b[i] - (n - done - cnt_a[i]))
    done += cnt_a[i] + cnt_b[i]


new_a = new_al + new_ar[::-1]
new_b = new_bl + new_br[::-1]
new = [[ai,bi] for ai,bi in zip(new_a,new_b)]


new.sort()

ans =[]
for ni in new:
    x,y = ni
    if(x==y):
        print('No')
        exit()
    ans.append(y)

print('Yes')
print(' '.join(map(str,ans)))