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
from sys import stdin, setrecursionlimit
from collections import deque
input = stdin.readline
setrecursionlimit(int(2e5))
def getstr(): return input()[:-1]
def getint(): return int(input())
def getints(): return list(map(int, input().split()))
def getint1(): return list(map(lambda x : int(x) - 1, input().split()))

adj = col = comp = []
cnt0 = cnt1 = 0

def dfs(us, cs, cmp, n):
    global adj, col, comp, cnt0, cnt1
    stack = [(us, cs)]
    inq = [False] * n
    inq[us] = True
    while len(stack) > 0:
        u, c = stack.pop()
        # print(u, c)
        inq[u] = False
        col[u] = c
        if col[u] == 0: cnt0 += 1
        else: cnt1 += 1
        comp[u] = cmp
        for v, ch in adj[u]:
            if col[v] == -1 and not inq[v]:
                inq[v] = True
                stack.append((v, c ^ ch))
    # print(col, comp)

def solve():
    global adj, col, comp, cnt0, cnt1
    n = getint()
    a = []
    pos = [[] for _ in range(n)]
    adj = [[] for _ in range(n)]
    for i in [0, 1]:
        a.append(getint1())
        for j, x in enumerate(a[i]):
            pos[x].append(j)
    for i, c in enumerate(pos):
        if len(c) != 2:
            print("-1")
            return
        if c[0] == c[1]: 
            continue
        r1 = int(a[0][c[0]] != i)
        r2 = int(a[0][c[1]] != i)
        adj[c[0]].append((c[1], int(r1 == r2)))
        adj[c[1]].append((c[0], int(r1 == r2)))
    # print(adj)
    col = [-1] * n
    comp = [-1] * n
    colcnt = []
    ans = cnt = 0
    # cnt = 0
    for i in range(n):
        if col[i] == -1:
            cnt0, cnt1 = 0, 0
            dfs(i, 0, cnt, n)
            cnt += 1
            colcnt.append((cnt0, cnt1))
            ans += min(cnt0, cnt1)
    # print(colcnt)

    print(ans)
    alist = []
    for i in range(n):
        chz = int(colcnt[comp[i]][0] < colcnt[comp[i]][1])
        if col[i] ^ chz:
            alist.append(i + 1)
    # print(len(alist))
    print(*alist)

if __name__ == "__main__":
    # solve()
    # for t in range(getint()):
    #     print("Case #{}: ".format(t + 1), end="")
    #     solve()
    for _ in range(getint()):
        solve()
