#include<bits/stdc++.h>
using namespace std;
int const N=1e5+10;
vector<int>a[N],s[N];
int ans,laf[N],g[N],dep[N];
void dfs(int x,int fa){
    int flg=0;
    for (auto v:a[x]){
        if (v==fa) continue;
        flg=1,dep[v]=dep[x]+1,dfs(v,x);
    }
    for (auto v:a[x]) if (laf[v]) ++g[x],s[x].push_back(v);
    if (!flg) laf[x]=1;
}
signed main(){
    freopen("hunter.in","r",stdin);
    freopen("hunter.out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0),cout.tie(0);
    int t;cin>>t;
    while (t--){
        int n;cin>>n;
        for (int i=1;i<=n;++i) a[i].clear(),laf[i]=g[i]=0,s[i].clear();
        ans=0;
        for (int i=1;i<n;++i){
            int u,v;cin>>u>>v;
            a[u].push_back(v);
            a[v].push_back(u);
        }
        int x=1;
        for (int i=1;i<=n;++i)
        	if (a[i].size()>1){x=i;break;}
        dep[x]=0,dfs(x,0);
        int j=0;
        for (int i=1;i<=n;++i) if (g[i]>g[j]) j=i;
        sort(g+1,g+n+1);
        if (!g[n-1]){
            int flg=0;
            for (auto v:s[j])
                if (dep[v]>2){
                    cout<<s[j].size()<<'\n';
                    flg=1;break;
                }
            if (!flg) cout<<"-1\n";
            continue;
        }
        int mx=0,sm=0;
        for (int i=1;i<=n;++i) mx=max(mx,g[i]),sm+=g[i];
        if (2*mx>=sm){
            int r=sm-g[n];
            g[n]-=r,sm-=r;
            cout<<sm<<'\n';
        }else{
            cout<<(sm+1)/2<<'\n';
        }
        /*int m=0;
        for (int i=1;i<=n;++i) m+=g[i];
        int l=1;
        for (int i=n;i>=1;--i){
            while (l+1<=i && !g[l]) ++l;
            if (l==i) break;
            int t=min(g[i],g[l]);
            g[i]-=t,g[l]-=t,m-=t;
            if (g[i]) ++i;
        }
        cout<<m<<'\n';*/
    }
    return 0;
}