#include<bits/stdc++.h>
using namespace std;
#define ll long long
vector<int> e[100000+10];

void solve()
{
	int n;
	cin>>n;
	for(int i=1;i<=n;i++)
	e[i].clear();
	for(int i=1;i<n;i++)
	{
		int u,v;
		cin>>u>>v;
		e[u].push_back(v);
		e[v].push_back(u);
	}
	queue<int> q;
	q.push(1);
	int root = 1;
	vector<int> dep(n+1),dep1(n+1);
	dep[1] = 1;
	while(!q.empty())
	{	int u = q.front();
		q.pop();
		for(auto x:e[u])
		{	if(dep[x])
			continue ;
			dep[x] = dep[u] +1;
			if(dep[x]>dep[root])
			root = x;
			q.push(x);
		}	
	}
	q.push(root);
	dep1[root] = 1;
	while(!q.empty())
	{
		int u = q.front();
		q.pop();
		for(auto x:e[u])
		{	if(dep1[x])
			continue;
			dep1[x] = dep1[u] +1;
			if(dep1[x]>dep1[root])
			root = x;
			q.push(x);
		}	
	}
	if(dep1[root]>3)
	{	int ans = 0;
		for(int i=1;i<=n;i++)
			if(e[i].size()==1)
				ans ++;
		cout<<ans-1<<endl;
	}
	else 
	{
		cout<<-1<<endl;
	}
}  
signed main (){
	std::ios::sync_with_stdio(false);  
	cin.tie(NULL); 
	cout.tie(NULL);
	int t;
	cin>>t;
	while(t--)
	solve();
}