#include <bits/stdc++.h>

#define endl '\n'
#define int long long

using namespace std;

const int maxn = 1e5 + 5;
const int maxm = 2e5 + 5;
int n;

int head[maxn], to[maxm], ne[maxm], idx;

void add(int x, int y) {
    ne[++idx] = head[x], head[x] = idx, to[idx] = y;
    ne[++idx] = head[y], head[y] = idx, to[idx] = x;
}

int in[maxn];
int dep[maxn];

void dfs(int fa, int i) {
    dep[i] = dep[fa] + 1;
    for (int e = head[i], id = to[e]; e; e = ne[e], id = to[e]) {
        if (id != fa)dfs(i, id);
    }
}

void solve() {
    cin >> n;
    idx = 0;
    for (int i = 1; i <= n; i++)head[i] = in[i] = 0;
    for (int i = 1, x, y; i < n; i++) {
        cin >> x >> y;
        add(x, y);
        in[x]++, in[y]++;
    }
    int rt;
    for (int i = 1; i <= n; i++) {
        if (in[i] == 1) {
            rt = i;
            break;
        }
    }
    dep[0] = -1;
    dfs(0, rt);
    vector<int> v;
    for (int i = 1; i <= n; i++) {
        if (in[i] == 1) {
            v.push_back(i);
        }
    }
    sort(v.begin(), v.end(), [](int x, int y) {
        return dep[x] < dep[y];
    });
    int cur = v.size() - 1, ans = 0;
//    cout<<rt<<endl;
//    cout<<v[0]<<" "<<v[cur]<<endl;
//    for(int i=1;i<=n;i++)cout<<dep[i]<<" ";
//    cout<<endl;
//    for(auto x:v)cout<<x<<","<<dep[x]<<endl;
//    cout<<endl;
    if (dep[v[0]] + dep[v[cur]] < 3) {
        cout << -1 << endl;
        return;
    }
    for (int i = 0, ed = cur; i <= cur; i++) {
        if (dep[v[i]] + dep[v[cur]] >= 3)ans++, cur--;
        else ans++;
    }
    cout << ans << endl;
}

signed main() {
//    freopen("../input.txt", "r", stdin);
    cin.tie(nullptr), cout.tie(nullptr);
    ios::sync_with_stdio(false);
    int test = 1;
    cin >> test;
    while (test--) {
        solve();
    }
    return 0;
}