You are given a table a of size 2 × n (i.e. two rows and n columns) consisting of integers from 1 to n.

In one move, you can choose some column j (1 ≤ j ≤ n) and swap values a_{1, j} and a_{2, j} in it. Each column can be chosen no more than once.

Your task is to find the minimum number of moves required to obtain permutations of size n in both first and second rows of the table or determine if it is impossible to do that.

You have to answer t independent test cases.

Recall that the permutation of size n is such an array of size n that contains each integer from 1 to n exactly once (the order of elements doesn't matter).

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of columns in the table. The second line of the test case contains n integers a_{1, 1}, a_{1, 2}, ..., a_{1, n} (1 ≤ a_{1, i} ≤ n), where a_{1, i} is the i-th element of the first row of the table. The third line of the test case contains n integers a_{2, 1}, a_{2, 2}, ..., a_{2, n} (1 ≤ a_{2, i} ≤ n), where a_{2, i} is the i-th element of the second row of the table.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case print the answer: -1 if it is impossible to obtain permutation of size n in both first and the second rows of the table, or one integer k in the first line, where k is the minimum number of moves required to obtain permutations in both rows, and k distinct integers pos_1, pos_2, ..., pos_k in the second line (1 ≤ pos_i ≤ n) in any order — indices of columns in which you need to swap values to obtain permutations in both rows. If there are several answers, you can print any.

Example

Input


6
4
1 2 3 4
2 3 1 4
5
5 3 5 1 4
1 2 3 2 4
3
1 2 1
3 3 2
4
1 2 2 1
3 4 3 4
4
4 3 1 4
3 2 2 1
3
1 1 2
3 2 2


Output


0

2
2 3 
1
1 
2
3 4 
2
3 4 
-1
import sys, math
import io, os
#data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from bisect import bisect_left as bl, bisect_right as br, insort
from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
#from itertools import permutations,combinations
def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var) : sys.stdout.write(' '.join(map(str, var))+'\n')
def out(var) : sys.stdout.write(str(var)+'\n')
#from decimal import Decimal
from fractions import Fraction
#sys.setrecursionlimit(100000)
INF = float('inf')
mod = int(1e9)+7


for t in range(int(data())):
    n=int(data())
    a1=mdata()
    a2=mdata()
    d=dd(int)
    g=[[] for i in range(n+1)]
    for i in range(n):
        d[a1[i]] += 1
        d[a2[i]] += 1
        if a1[i]==a2[i]:
            continue
        g[a1[i]].append((a2[i],i+1,0))
        g[a2[i]].append((a1[i],i+1,1))
    if max(d.values())>2:
        out(-1)
        continue
    vis=[0]*(n+1)
    vis1=[0]*(n+1)
    ans=[]
    for i in range(1,n+1):
        if vis[i]==0 and g[i]:
            s=[[],[]]
            vis[i]=1
            s[g[i][0][2]].append(g[i][0][1])
            s[1-g[i][1][2]].append(g[i][1][1])
            vis[g[i][0][0]] = -1
            vis[g[i][1][0]] = 1
            vis1[g[i][0][1]] = 1
            vis1[g[i][1][1]] = 1
            q=[]
            q.append(g[i][0][0])
            q.append(g[i][1][0])
            while q:
                a=q.pop()
                if vis[a]==1:
                    for nei in g[a]:
                        if vis1[nei[1]]==0:
                            s[1-nei[2]].append(nei[1])
                            vis[nei[0]] = -1
                            vis1[nei[1]] = 1
                            q.append(nei[0])
                else:
                    for nei in g[a]:
                        if vis1[nei[1]]==0:
                            s[1-nei[2]].append(nei[1])
                            vis[nei[0]] = 1
                            vis1[nei[1]] = 1
                            q.append(nei[0])
            if len(s[0])<len(s[1]):
                ans+=s[0]
            else:
                ans+=s[1]
    out(len(ans))
    outl(ans)




