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<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % mod;
		x = x * x % mod; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

struct ste {
	int id, fr; bool f;
};
void solve() {
	int n; cin >> n;
	vector<set<int>> g(n), h(n);
	rep(i, n - 1) {
		int a, b; cin >> a >> b; a--; b--;
		g[a].insert(b);
		g[b].insert(a);
	}
	rep(i, n - 1) {
		int a, b; cin >> a >> b; a--; b--;
		h[a].insert(b);
		h[b].insert(a);
	}

	int ans = mod;
	rep(s, n) {
		if (g[s].size() == 1) {
			rep(to, n) {
				if (s == to)continue;
				int cost = 0;
				if (*g[s].begin() != to)cost = 1;

				vector<bool> ers(n, false);
				vector<int> chs(n, 0);
				vector<int> par(n);
				vector<ste> v;
				if (h[s].count(to)) {
					v.push_back({ to,s,false });
				}
				else {
					v.push_back({ to,s,true });
				}


				bool valid = true;
				while (!v.empty()) {
					ste st = v.back(); v.pop_back();
					par[st.id] = st.fr;
					if (st.f) {
						ers[st.id] = true; cost++;
					}
					for (int nex : g[st.id]) {
						if (nex == st.fr)continue;
						if (nex == s) {
							continue;
						}
						if (h[st.id].count(nex)) {
							v.push_back({ nex,st.id,st.f });
						}
						else {
							v.push_back({ nex,st.id,true });
						}
						chs[st.id]++;
					}
				}

				while (true) {
					bool upd = false;
					rep(i, n)if (ers[i]) {
						if (chs[i] == 0) {
							vector<int> tos;
							for (int hto : h[i]) {
								if (!ers[hto]) {
									tos.push_back(hto);
								}
							}
							if (tos.empty())continue;
							if (tos.size() >= 2) {
								valid = false; break;
							}
							if (tos.size() == 1) {
								ers[i] = false;
								chs[par[i]]--;
								upd = true;
								break;
							}
						}
					}
					if (!upd)break;
				}
				rep(i, n)if (ers[i])valid = false;
				if (valid)ans = min(ans, cost);
			}



		}
	}
	if (ans == mod)ans = -1;
	cout << ans << "\n";

}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init();
	int t; cin >> t; rep(i, t)
	solve();
	return 0;
}