#include<bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pf push_front
#define LC k<<1
#define RC k<<1|1
#define IO cin.sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define all(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define rep(i,a,n) for (int i = a; i < n; i++)
#define repn(i,a,n) for (int i = a; i <= n; i++)
#define per(i,a,n) for (int i = (n) - 1; i >= a; i--)
#define pern(i,a,n) for (int i = n; i >= a; i--)

typedef long long LL;
typedef long double LD;
typedef unsigned long long ull;
typedef pair<int, int> PII;
typedef pair<int, LL> PIL;
typedef pair<LL, int> PLI;
typedef pair<double, double> PDD;
typedef pair<ull, ull> PUU;
typedef pair<LL, LL> PLL;

const int N = 110000;
const int M = 1100000;
const int mod = 1e9+7;
const int inf = (int)1e9;
const LL INF = 1e18;
const double eps = 1e-9;

mt19937_64 Rand((unsigned long long)new char);
#define rand Rand

int T, n, sz[N], dp[N], rt, du[N], mx, ans;
PII v[N];
vector<int> g[N];
void dfs(int x, int fa) {
	if (du[x] == 1) sz[x] = 1;
	else sz[x] = 0;
	v[x] = mp(0, 0);
	int num = 0;
	for (auto y: g[x]) {
		if (y != fa) {
			dfs(y, x), sz[x] += sz[y];
			if (du[y] == 1) num++;
			else v[x] = max(v[x], mp(sz[y], y));
		}
	}
	if (num) v[x] = max(v[x], mp(num, x));
}
int work(int x, int fa, int delta) {
	if (v[x].fi * 2 <= sz[x] + delta * 2) {	
		return (sz[x] - delta) / 2 + ((sz[x] - delta) % 2);
	}
	if (v[x].se == x) return max(v[x].fi - delta, 0);
	return work(v[x].se, x, delta + sz[x] - v[x].fi);
}
int main() {
	IO;
	cin >> T;
	while (T--) {
		cin >> n;
		repn(i, 1, n) g[i].clear(), du[i] = 0;
		rep(i, 1, n) {
			int x, y;
			cin >> x >> y;
			g[x].pb(y), g[y].pb(x);
			du[x]++, du[y]++;
		}
		if (n <= 3) {
			cout << "-1\n";
			continue;
		}
		mx = 0;
		repn(i, 1, n) {
			if (du[i] > 1) rt = i;
			mx = max(mx, du[i]);
		}
		if (mx == n - 1) {
			cout << "-1\n";
			continue;
		}
		ans = 0;
		dfs(rt, 0);
		cout << work(rt, 0, 0) << "\n";
	}
	return 0;
}