Problem: Snuke has found two trees A and B, each with N vertices numbered 1 to N. The i-th edge of A connects Vertex a_i and b_i, and the j-th edge of B connects Vertex c_j and d_j. Also, all vertices of A are initially painted white.

Snuke would like to perform the following operation on A zero or more times so that A coincides with B:

* Choose a leaf vertex that is painted white. (Let this vertex be v.)
* Remove the edge incident to v, and add a new edge that connects v to another vertex.
* Paint v black.



Determine if A can be made to coincide with B, ignoring color. If the answer is yes, find the minimum number of operations required.

You are given T cases of this kind. Find the answer for each of them.

Constraints

* 1 \leq T \leq 20
* 3 \leq N \leq 50
* 1 \leq a_i,b_i,c_i,d_i \leq N
* All given graphs are trees.

Input

Input is given from Standard Input in the following format:


T
case_1
:
case_{T}


Each case is given in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_{N-1} d_{N-1}


Output

For each case, if A can be made to coincide with B ignoring color, print the minimum number of operations required, and print `-1` if it cannot.

Examples

Input

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


Output

1
-1


Input

3
8
2 7
4 8
8 6
7 1
7 3
5 7
7 8
4 2
5 2
1 2
8 1
3 2
2 6
2 7
4
1 2
2 3
3 4
3 4
2 1
3 2
9
5 3
4 3
9 3
6 8
2 3
1 3
3 8
1 7
4 1
2 8
9 6
3 6
3 5
1 8
9 7
1 6


Output

6
0
7

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 59;

void set_min(int &a, int b) {
    if (a == -1 || b != -1 && b < a) a = b;
}

int N;

struct Graph {
    vector<int> edge[MAX_N];

    void add_edge(int a, int b) { edge[a].push_back(b); }

    void add_edge_bi(int a, int b) { add_edge(a, b); add_edge(b, a); }

    void erase_edge(int a, int b) { edge[a].erase(find(edge[a].begin(), edge[a].end(), b)); }

    void erase_edge_bi(int a, int b) { erase_edge(a, b); erase_edge(b, a); }

    void get_pa_dfs(int x, int pa[]) {
        for (int i : edge[x]) {
            if (pa[i]) continue;
            pa[i] = x;
            get_pa_dfs(i, pa);
        }
    }

    void get_pa(int s, int pa[]) {
        fill_n(pa + 1, N, 0);
        pa[s] = -1; get_pa_dfs(s, pa);
    }

    void acyclic_dfs(int x, int deg[]) {
        deg[x] = -1;
        for (int i : edge[x]) {
            if (!--deg[i]) {
                acyclic_dfs(i, deg);
            }
        }
    }

    bool acyclic() {
        int deg[MAX_N];
        fill_n(deg + 1, N, 0);
        for (int i = 1; i <= N; i++)
            for (int j : edge[i])
                deg[j]++;
        for (int i = 1; i <= N; i++)
            if (deg[i] == 0)
                acyclic_dfs(i, deg);
        for (int i = 1; i <= N; i++)
            if (deg[i] != -1)
                return false;
        return true;
    }
};

int get_same(int x, int root, int a_pa[], int b_pa[], int same[]) {
    int &res = same[x];
    if (res != -1) return res;
    if (x == root) return res = 1;
    if (a_pa[x] != b_pa[x]) return res = 0;
    return res = get_same(a_pa[x], root, a_pa, b_pa, same);
}

int solve(Graph tree_s, Graph tree_t, int root, int base = 0) {
    int s_pa[MAX_N], t_pa[MAX_N], same[MAX_N];
    tree_s.get_pa(root, s_pa);
    tree_t.get_pa(root, t_pa);
    for (int i = 1; i <= N; i++) same[i] = -1;
    for (int i = 1; i <= N; i++) get_same(i, root, s_pa, t_pa, same);
    Graph constraints;
    for (int i = 1; i <= N; i++) {
        if (same[i]) continue;
        if (!same[s_pa[i]])
            constraints.add_edge(i, s_pa[i]);
        if (!same[t_pa[i]])
            constraints.add_edge(t_pa[i], i);
    }
    if (constraints.acyclic()) {
        int res = base;
        for (int i = 1; i <= N; i++) res += 1 - same[i];
        return res;
    }
    return -1;
}

void solve() {
    Graph tree_s, tree_t;
    scanf("%d", &N);
    for (int i = 1; i < N; i++) {
        int a, b; scanf("%d%d", &a, &b);
        tree_s.add_edge_bi(a, b);
    }
    for (int i = 1; i < N; i++) {
        int a, b; scanf("%d%d", &a, &b);
        tree_t.add_edge_bi(a, b);
    }
    int ans = -1;
    for (int i = 1; i <= N; i++) {
        set_min(ans, solve(tree_s, tree_t, i));
        if (tree_s.edge[i].size() == 1) {
            for (int j = 1; j <= N; j++) {
                if (i == j) continue;
                Graph tree_m = tree_s;
                tree_m.erase_edge_bi(i, tree_s.edge[i][0]);
                tree_m.add_edge_bi(i, j);
                set_min(ans, solve(tree_m, tree_t, i, 1));
            }
        }
    }
    printf("%d\n", ans);
}

int main() {
    int T; scanf("%d", &T);
    for (int i = 1; i <= T; i++) {
        solve();
    }
}