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
from collections import deque

input=sys.stdin.readline
#sys.setrecursionlimit(2*10**5)

for _ in range(int(input())):
    n=int(input())
    a=list(map(int,input().split()))
    b=list(map(int,input().split()))
    data=[[] for i in range(n)]
    for i in range(n):
        data[a[i]-1].append(i)
        data[b[i]-1].append(i)
    for i in range(n):
        if len(data[i])!=2:
            print(-1)
            break
    else:
        edge=[[] for i in range(n)]
        for i in range(n):
            u,v=data[i][0],data[i][1]
            edge[u].append((v,i))
            edge[v].append((u,i))

        seen=[False]*n
        temp=[]
        res=0
        def dfs(v,cond):
            global temp,res
            res.append(v)
            if cond==1:
                up,down=a[v],b[v]
            else:
                up,down=b[v],a[v]

            for nv,val in edge[v]:
                if not seen[nv]:
                    seen[nv]=True
                    if a[nv]==up or b[nv]==down:
                        temp.append(nv)
                        dfs(nv,-1)
                    else:
                        dfs(nv,1)

        def bfs(i):
            global temp,res
            deq=deque([(i,1)])
            while deq:
                v,cond=deq.popleft()
                res.append(v)
                if cond==1:
                    up,down=a[v],b[v]
                else:
                    up,down=b[v],a[v]

                for nv,val in edge[v]:
                    if not seen[nv]:
                        seen[nv]=True
                        if a[nv]==up or b[nv]==down:
                            temp.append(nv)
                            deq.append((nv,-1))
                        else:
                            deq.append((nv,1))

        ans=[]
        for i in range(0,n):
            if not seen[i]:
                res=[]
                temp=[]
                seen[i]=True
                bfs(i)
                if len(res)-len(temp)>=len(temp):
                    ans+=temp
                else:
                    temp=set(temp)
                    for v in res:
                        if v not in temp:
                            ans.append(v)
        if ans:
            ans=[ans[i]+1 for i in range(len(ans))]
        print(len(ans))
        print(*ans)
