#include <bits/stdc++.h>

#define forn(i, n) for(int i = 0; i < (int)n; ++i)
#define for1(i, n) for(int i = 1; i <= (int)n; ++i)
#define fore(i, l, r) for(int i = (int)l; i <= (int)r; ++i)
#define all(x) x.begin(), x.end()
#define el '\n'
#define d(x) cerr << #x << ' ' << x << el

#define sz(a) (int) a.size()
#define pb push_back
using namespace std;


typedef vector<int> vi;
typedef array<int, 4> a4;
const int nax = 2e5;
// const int nax = 2e3;
vi g[nax];
int sobra[nax], dist[2][nax];
int ans = 0;
void dfs(int u, int p = -1){
    // d(u),d(p);
    vi pasar;
    int cnt = 0;

    for(int v : g[u]){
        if(v == p)continue;
        dfs(v,u);
        pasar.pb(sobra[v]);
        cnt+=sobra[v];
    }
    if(sz(g[u]) == 1){ 
        sobra[u] = 1;
        ++ans;
        return;
    }

    sort(all(pasar), greater<int> ());
    int grand = pasar[0];
    int left = 0;
    if(grand <= cnt - grand){
        left = cnt & 1;
        ans -= cnt / 2;
    }else{
        left = grand - (cnt - grand);
        ans -= (cnt - grand);
    }
    sobra[u] = left;
}

int curMax = -1, mxDist = -1;
void diam(int u, int &idx,  int p = -1){

    for(int v : g[u]){
        if(v == p)continue;
        dist[idx][v] = dist[idx][u] + 1;
        if(dist[idx][v] > mxDist){
            mxDist = dist[idx][v];
            curMax = v;
        }
        diam(v, idx, u);
    }
}
void solve(){
    int n;
    cin>>n;
    ans = 0;
    forn(i,n) g[i].clear(), sobra[i] = 0, dist[0][i] = dist[1][i] = 0;
    forn(i,n-1){
        int u,v;
        cin>>u>>v;
        --u,--v;
        g[u].pb(v);
        g[v].pb(u);
    }
    if(n == 2){
        cout<<"-1"<<el;
        return;
    }
    int root = 0;
    forn(i,n) if(sz(g[i]) > 1) root = i;
    dfs(root);

    curMax = 0, mxDist = 0;
    int idx = 0;
    diam(curMax, idx);
    mxDist = 0;
    // d(curMax);
    diam(curMax, ++idx);
    // d(curMax);
    // d(mxDist);
    if(mxDist <= 2){
        cout<<"-1"<<el;
    }else
        cout<<ans<<el;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int tt;
    cin>>tt;
    while(tt--){
        solve();
    }
}