#include <bits/stdc++.h>

#define forn(i,n) for(int i=0; i < n; ++i)
#define pb push_back
#define el '\n'
#define sz(v) int(v.size())

using namespace std;

typedef vector<int> vi;
const int N = 2e5 + 10;
vi g[N];

void borre(int n){
  forn(i, n) g[i].clear();
}

int main(){
  ios_base::sync_with_stdio(0); cin.tie(0);
  int t; cin >> t;
  while(t--){
    int n; cin >> n;
    forn(i, n-1){
      int u, v; cin >> u >> v;
      --u, --v;
      g[u].pb(v);
      g[v].pb(u);
    }

    vi cnt(n);
    forn(i, n){
      if(sz(g[i]) == 1){
        cnt[g[i][0]]++;
      }
    }

    priority_queue<int, vi, greater<int>> pq;
    forn(i, n){
      if(cnt[i]) pq.push(cnt[i]);
    }

    if(n == 2 || sz(pq) == 1){
      cout << -1 << el;
      borre(n);
      continue;
    }

    int ans = 0;
    while(sz(pq) > 1){
      ++ans;
      int c1 = pq.top(); pq.pop();
      int c2 = pq.top(); pq.pop();
      --c1, --c2;
      if(c1) pq.push(c1);
      if(c2) pq.push(c2);
    }
    if(sz(pq)) ans += pq.top();
    cout << ans << el;
    borre(n);
  }
}