#include <bits/stdc++.h>

#define ll long long

using namespace std;

int par[10001];
int rank_aa[10001];

void init(int n)
{
	for(int i=0;i<n;i++){
		par[i] = i;
		rank_aa[i] = 0;
	}
}

int find(int x)
{
	if (par[x]==x){
		return x;
	}else{
		return par[x] = find(par[x]);
	}
}

void unite(int x, int y)
{
	x = find(x);
	y = find(y);
	if (x == y) return;
	if (rank_aa[x] < rank_aa[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if (rank_aa[x] == rank_aa[y]) rank_aa[x]++;
	}
}

bool same(int x, int y)
{
	return find(x) == find(y);
}

struct edge{ll u, v, cost;};

bool comp(const edge& x, const edge& y){
	return x.cost < y.cost;
}

edge es[10001];
ll V, E;

int main() {
	while(cin>>V>>E, V>0){
		for(int i=0; i<E; i++){
			int s, t, c; cin>>s>>t>>c;
			es[i].u = s-1;
			es[i].v = t-1;
			es[i].cost = c;
		}
		sort(es, es+E, comp);
		init(V);
		vector<int> ans;
		for(int i=0; i<E; i++){
			edge e = es[i];
			if (!same(e.u, e.v)){
				unite(e.u, e.v);
				ans.push_back(e.cost);
			}
		}
		ll mid;
		mid = ans[ans.size()/2];
		cout << mid << "\n";
	}
	return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

Problem Statement

You are given a connected undirected graph which has even numbers of nodes. A connected graph is a graph in which all nodes are connected directly or indirectly by edges.

Your task is to find a spanning tree whose median value of edges' costs is minimum. A spanning tree of a graph means that a tree which contains all nodes of the graph.



Input

The input consists of multiple datasets.

The format of each dataset is as follows.


n m
s_1 t_1 c_1
...
s_m t_m c_m


The first line contains an even number n (2 \leq n \leq 1,000) and an integer m (n-1 \leq m \leq 10,000). n is the nubmer of nodes and m is the number of edges in the graph.

Then m lines follow, each of which contains s_i (1 \leq s_i \leq n), t_i (1 \leq s_i \leq n, t_i \neq s_i) and c_i (1 \leq c_i \leq 1,000). This means there is an edge between the nodes s_i and t_i and its cost is c_i. There is no more than one edge which connects s_i and t_i.

The input terminates when n=0 and m=0. Your program must not output anything for this case.

Output

Print the median value in a line for each dataset.

Example

Input

2 1
1 2 5
4 6
1 2 1
1 3 2
1 4 3
2 3 4
2 4 5
3 4 6
8 17
1 4 767
3 1 609
8 3 426
6 5 972
8 1 607
6 4 51
5 1 683
3 6 451
3 4 630
8 7 912
3 7 43
4 7 421
3 5 582
8 4 538
5 7 832
1 6 345
8 2 608
0 0


Output

5
2
421

### Response

```cpp
#include <bits/stdc++.h>

#define ll long long

using namespace std;

int par[10001];
int rank_aa[10001];

void init(int n)
{
	for(int i=0;i<n;i++){
		par[i] = i;
		rank_aa[i] = 0;
	}
}

int find(int x)
{
	if (par[x]==x){
		return x;
	}else{
		return par[x] = find(par[x]);
	}
}

void unite(int x, int y)
{
	x = find(x);
	y = find(y);
	if (x == y) return;
	if (rank_aa[x] < rank_aa[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if (rank_aa[x] == rank_aa[y]) rank_aa[x]++;
	}
}

bool same(int x, int y)
{
	return find(x) == find(y);
}

struct edge{ll u, v, cost;};

bool comp(const edge& x, const edge& y){
	return x.cost < y.cost;
}

edge es[10001];
ll V, E;

int main() {
	while(cin>>V>>E, V>0){
		for(int i=0; i<E; i++){
			int s, t, c; cin>>s>>t>>c;
			es[i].u = s-1;
			es[i].v = t-1;
			es[i].cost = c;
		}
		sort(es, es+E, comp);
		init(V);
		vector<int> ans;
		for(int i=0; i<E; i++){
			edge e = es[i];
			if (!same(e.u, e.v)){
				unite(e.u, e.v);
				ans.push_back(e.cost);
			}
		}
		ll mid;
		mid = ans[ans.size()/2];
		cout << mid << "\n";
	}
	return 0;
}

```